Field-based similarity search system and method

ABSTRACT

A field-based similarity search system includes an input device which inputs a query molecule, and a processor which partitions a conformational space of the query molecule into a fragment graph including an acyclic graph including plural fragment nodes connected by rotatable bond edges, computes a property field on fragment pairs of fragments of the query molecule from the fragment graph, the property field including a local approximation of a property field of the query molecule, constructs a set of features of the fragment pairs based on the property field, the features including a set of local, rotationally invariant, and moment-based descriptors generated from all conformations of the fragment graph of the query molecule, and weights the descriptors according to importance as perceived from a training set of descriptors to generate a context-adapted descriptor-to-key mapping which maps the set of descriptors to a set of feature keys.

CROSS REFERENCE TO RELATED APPLICATIONS

The present Application is a Continuation Application of U.S. patentapplication Ser. No. 13/113,256. filed on May 23, 2011 now U.S. Pat. No.8,306,755, which was a Divisional Application of U.S. patent applicationSer. No. 12/544,889 filed on Aug. 20, 2009 now U.S. Pat. No. 8,014,990,which was a Divisional Application of U.S. patent application Ser. No.10/102.902 filed on Mar. 22, 2002 now abandoned, which claims thebenefit of Provisional Application No. 60/278,260 which was filed onMar. 23, 2001, and which are incorporated herein by reference.

This Application is related to U.S. Pat. No. 6,349.265 assigned toInternational Business Machines Corporation, and U.S. patent applicationSer. No. 09/275,568 filed on Mar. 24, 1999 (assigned to InternationalBusiness Machines Corporation and having assignee's, which are alsoincorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to a field-based similaritysearch system and method, and more particularly, a field-basedsimilarity search system and method which identifies similar moleculesbased on fragment pair feature similarities.

2. Description of the Related Art

An important problem in drug discovery efforts is finding molecules thathave a similar function to a molecule known to be active towards abiological target or that elicits a biological response of interest.Commonly, such detailed structural information of the mechanism ofaction is unknown. Although, there exist several conventional methods tosearch for or create such compounds, the most common involves aconjectured conformation of the molecule of interest (e.g., querymolecule), or the repeated application of a method to a series of queryconformers.

More specifically, there exist several conventional methods of aligninga group of flexible molecules to a particular query conformation (e.g.,molecular superposition) using computer-assisted drug design (see, e.g.,C. Lemmen, T. Lengauer, and G. Klebe, FLEXS: A method for fast flexibleligand superposition. Journal of Medicinal Chemistry, 41:4502-4520,1998; Michael D. Miller, Robert P. Sheridan, and Simon K. Kearsley, Sq:A program for rapidly producing pharmacophorically relevent molecularsuperpositions, J. Med. Chem., 42:1505-1514, 1999; Christian Lemmen,Claus Hiller, and Thomas Lengauer, Rigfit: a new approach tosuperimposing ligand molecules. Journal of Computer-Aided MolecularDesign, 11:357 368, 1997; Gerhard Klebe, Thomas Mietzner, and FrankWeber, Different approaches toward an automatic structural alignment ofdrug molecules: Applications to sterol mimics, thrombin and thermolysininhibitors, Journal of Computer-Aided Molecular Design, 8:751 778, 1994;Simon K. Kearsley and Graham M. Smith, An alternative method for thealignment of molecular structures: maximizing electrostatic and stericoverlap, Journal of Computer Aided Molecular Design, 8:565 582, 1994;Colin McMartin and Regine S. Bohacek, Flexible matching of test ligandsto a 3d pharmacophore using a molecular superposition force field:Comparison of predicted and experimental conformations of inhibitors ofthree enzymes. J. Med. Chem., 42:1505 1514, 1999; S. Handschuh, M.Wagnener, and J. Gasteiger, Superposition of three-dimensional chemicalstructures allowing for conformational flexibility by a hybrid method,J. Chem. Inf Comput. Sci., 38:220-232, 1998; J. Mestres. D. C. Rohrer,and G. M. Maggiora, A molecular field-based similarity approach topharmacophoric pattern recognition, J. Mol. Graph. Modeling, 15:114-21,1997; Y. C. Martin, M. G. Bures, E. A. Danaher, J. DeLazzer, J. Lico,and P. A. Pavlik, A fast new approach to pharmacophore mapping and itsapplication to dopaminergic and benzodiazepine agonists, Journal ofComputer Aided Molecular Design, 7:83-102, 1993; Peter Willett,Searching for pharmacophoric patterns in databases of three dimensionalchemical structures, Journal of Molecular Recognition, 8:290-303, 1995;Gareth Jones, Peter Willett, and Robin C. Glen, A genetic algorithm forflexible molecular overlay and pharmacophore elucidation, J.Comput.-Aided Mal. Des., 9:532-549, 1995; D. A. Thorner, D. J. Wild, P.Willett, and P. M. Wright, Similarity searching in files ofthree-dimensional chemical structures: flexible field-based searching ofmolecular electrostatic potentials, Journal of Chemical Information andComputer Sciences, 36:900 908, 1996; D. J. Wild and P. Willett.Similarity searching in files of 3-dimensional chemicalstructures—alignment of molecular electrostatic potential fields with agenetic algorithm, Journal of Chemical Information and ComputerSciences, 36:159-167, 1996; David A. Thorner, Peter Willett, Robert C.Glen, P. M. Wright, and Robin Taylor, Similarity searching in files ofthree-dimensional chemical structures” representation and searching ofmolecular electrostatic potentials using field-graphs, J. Comput.-AidedMol. Des., 1:163 174, 1997; and Gerhard Klebe, Structural alignment ofmolecules, In Hugo Kubinyi, editor, 3D QSAR in Drug Design, pages173-199. ESCOM, Leiden, 1993).

In the absence of structural information regarding the ligand receptoror ligand-enzyme complex, structural alignment is a way of bothelucidating important features responsible for activity (Ki Hwan Kim,List of comfa references 1993-1997, In Hugo Kubinyi, Gerd Folkers, andYvonne C. Martin, editors, 3D QSAR in Drug Design, volume 3, pages 317338, Kluwer, Dordrecht/Boston/London, 1998; and Gerhard Klebe,Comparative molecular similarity indicies analysis, In Hugo Kubinyi,Gerd Folkers, and Yvonne C. Martin, editors, 3D QSAR in Drug Design,volume 3, pages 87-104, Kluwer, Dordrecht/Boston/London, 1998) and ameans of finding new molecules with similar or better activity (MichaelD. Miller, Robert P. Sheridan, and Simon K. Kearsley, Sq: A program forrapidly producing pharmacophorically relevent molecular superpositions,J. Med. Chem., 42:1505-1514, 1999; Andrew C. Good and Jonathan S. Mason,Three dimensional structure database searches, In Kenny B. Lipkowitz andDonald B. Boyd, editors, Reviews in Computational Chemistry, volume 7,chapter 2, pages 67 117. VCH Publishers, Inc., New York, 1996; and PeterWillett, Searching for pharmacophoric patterns in databases of threedimensional chemical structures, Journal of Molecular Recognition,8:290-303, 1995).

Generally, when one is attempting to elucidate spatial and chemicalinformation about the nature of the host ligand interaction, one oftenbegins with the alignment of a series of active compounds based on somekind of alignment rule. Unfortunately, this process is riddled withdifficulties and assumptions about the relevant conformations, relevantfeatures, importance of internal strain, the role of hydrogen bonds,electrostatics, solvation and hydrophobicity, as well as more profoundconcerns such as whether compounds in a data set even bind at thereceptor site via the same mechanism. It is clear that no single methodfor alignment will settle these issues across widely varying contexts.

Several conventional superposition methods reported are field-based(see, e.g., Michael D. Miller, Robert P. Sheridan, and Simon K.Kearsley, Sq: A program for rapidly producing pharmacophoricallyrelevent molecular superpositions, J. Med. Chem., 42:1505-1514, 1999;Christian Lemmen, Claus Hiller, and Thomas Lengauer, Rigfit: a newapproach to superimposing ligand molecules, Journal of Computer-AidedMolecular Design, 11:357 368, 1997; J. Mestres. D. C. Rohrer, and G. M.Maggiora, A molecular field-based similarity approach to pharmacophoricpattern recognition, J. Mol. Graph. Modeling, 15:114-21, 1997; and D. A.Thorner, D. J. Wild, P. Willett, and P. M. Wright, Similarity searchingin files of three-dimensional chemical structures: flexible field-basedsearching of molecular electrostatic potentials, Journal of ChemicalInformation and Computer Sciences, 36:900 908, 1996). An attractiveaspect of field-based approaches is the potential for incorporating highlevels of theory into the field. Apart from the difficulties and expenseof deploying high level quantum mechanical calculations, the design of asystem that can utilize the results of such calculations for use insimilarity analysis is considered forward looking.

However, such conventional field-based approaches are confined to aparticular field definition. For example, a conventional system designedfor simplistic, phenomenological fields, is not available for fieldsderived from quantum mechanical calculations. This severely limits theversatility of these conventional systems.

SUMMARY OF THE INVENTION

In view of the foregoing, and other problems, disadvantages, anddrawbacks of conventional systems and methods, the present invention hasbeen devised having as its objective, to provide a fast and efficientfield-based similarity search system and method.

The present invention includes a field-based similarity search systemwhich includes a database for storing at least one candidate molecule,an input device for inputting a query molecule, and a processor foridentifying a candidate molecule which is similar to the query moleculebased on a similarity of fragment pair features.

Specifically, the processor may identify a feature of a query moleculefragment pair. The processor may also match a query molecule fragmentpair feature with a candidate molecule fragment pair feature, andretrieve a candidate molecule fragment pair having at least apredetermined number of matching features.

Further, the processor may align retrieved fragment pairs using a poseclustering method. The processor may also construct a fully alignedcandidate molecule by assembling retrieved fragment pairs. The processormay also generate the fragment pair for the query molecule.

In addition, the inventive system may include a display device fordisplaying an output from the processor. The system may also include amemory device for storing a query molecule fragment pair feature.Further, the memory device may store data and instructions to beexecuted by the processor.

More specifically, the fragment pair may include two neighboringfragments connected by a rotatable bond at a specific dihedral angle.Further, the feature may include a generalization of a CoMMA descriptor.

In another aspect, the present invention includes an inventivefield-based similarity search method which includes generating aconformational space representation and an arbitrary description of athree-dimensional property field for a flexible molecule, characterizingparts of the flexible molecule and representing a query molecule usingthe arbitrary description for a comparison with the conformational spacerepresentation, and aligning the parts to the query molecule andassembling the parts to form an alignment onto the query molecule.

Alternatively, the inventive field-based similarity search method mayinclude identifying a feature of a query molecule fragment pair,matching a query molecule fragment pair feature with a candidatemolecule fragment pair feature; and retrieving a candidate moleculefragment pair having at least a predetermined number of matchingfeatures.

Alternatively, the inventive field-based similarity search method mayinclude a method for finding alignments of a flexible molecule to aquery molecule. The method may include, representing a conformationspace of the flexible molecule, generating an arbitrary description of athree-dimensional property field of the flexible molecule,characterizing parts of the flexible molecule using the arbitrarydescription, representing a query molecule using the arbitrarydescription for a comparison with molecules represented by theconformation space, aligning the parts of the flexible molecule to thequery molecule, and assembling the parts of the flexible molecule toform an alignment thereof onto the query molecule.

In another aspect, the present invention includes a programmable storagemedium tangibly embodying a program of machine-readable instructionsexecutable by a digital processing apparatus to perform a similaritysearch method, the method including generating a conformational spacerepresentation and an arbitrary description of a three-dimensionalproperty field for a flexible molecule, characterizing parts of theflexible molecule and representing a query molecule using the arbitrarydescription for a comparison with the conformational spacerepresentation, and aligning the parts to the query molecule andassembling the parts to form an alignment onto the query molecule.

With its unique and novel features, the present invention provides afast and efficient field-based similarity search system and method whichare not confined to a particular field definition. For example, theinventive system and method may be designed for simplistic,phenomenological fields, as well as for fields derived from quantummechanical calculations. Therefore, the claimed system and methodprovides improved versatility over conventional systems and methods.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, aspects and advantages will be betterunderstood from the following detailed description of a preferredembodiment of the invention with reference to the drawings, in which:

FIG. 1 illustrates a schematic diagram of an inventive field-basedsimilarity search system 100 according to the present invention;

FIG. 2 illustrates a fragmentation and conformational expansion ofmethotrexate;

FIG. 3 illustrates a schematic representation of a fragment graph;

FIG. 4 illustrates Table I which provides the signs of axes which may bechosen to fix a sensing according to the present invention;

FIG. 5 illustrates Table II which shows the number of components whichmay be present in an sample descriptor;

FIG. 6 illustrates a graph showing the distribution of features aftermapping into a 2-dimensional space by way of discriminant analysis;

FIG. 7(A) illustrates a dihydrofolate molecule and FIG. 7(B) illustratesa methotrexate molecule;

FIG. 8 illustrates Table III which shows experimental parameters used bythe inventors;

FIG. 9 illustrates a Fisher discriminant matrix;

FIG. 10 illustrates Table IV which has cells corresponding torectangular bins from which the discriminant space is partitioned,according to the present invention;

FIG. 11(A) illustrates a dihydrofolate molecule having the featureslabeled by the name of the central atom of the corresponding scoop, andFIG. 11(B) illustrates a methotrexate molecule having the featureslabeled by the name of the central atom of the corresponding scoop;

FIG. 12 illustrates Table V which shows the distribution of thecorrespondence cluster sizes for rigid body superposition of the crystalstructure of methotrexate onto that of dihydrofolate;

FIG. 13 illustrates Table VI which shows the statistics for the fragmentand fragment pair partitioning of methotrexate;

FIG. 14 illustrates Table VIII which shows the distribution of thecorrespondence cluster sizes for flexible superposition of methotrexateonto the crystal structure of dihydrofolate;

FIG. 15 illustrates the number of bases that survive each assembly phasefor the flexible superposition of methotrexate onto the crystalstructure of dihydrofolate;

FIG. 16 illustrates a flexible alignment of methotrexate onto thecrystal structure of dihydrofolate generated by the inventive system100;

FIG. 17 illustrates a flexible alignment of methotrexate onto thecrystal structure of dihydrofolate where the pteridine ring is flippedby 180°, which was generated by the inventive system 100;

FIG. 18 illustrates a flexible alignment of methotrexate onto thecrystal structure of dihydrofolate where the aromatic rings are skewedwith respect to each other, which was generated by the inventive system100;

FIG. 19 illustrates Table IX which shows the fragmentation statistics onthe additional molecules added to the database, in the inventors'experiments;

FIG. 20 illustrates sixteen additional structures added to the databasecontaining methotrexate, in the inventors' experiments;

FIG. 21 illustrates Table X which shows each molecule's distribution ofcorrespondence cluster sizes for fragment pair alignments;

FIG. 22 illustrates Table XI which shows the distribution of clustersizes for the DHFR inhibitors;

FIG. 23 illustrates Table XII which shows the alignment and assemblytimings, top Carbo scores, and total number of candidates for eachligand investigated;

FIG. 24 illustrates Table XIII which shows the alignment and assemblytimings, top Carbo scores, and total number of candidates for the eightDHFR inhibitors investigated;

FIG. 25 is a bar graph showing the percentage of clusters by moleculesfor each cluster size;

FIG. 26 is a flow chart illustrating an inventive field-based similaritysearch method 200 according to the present invention;

FIG. 27 illustrates a typical hardware configuration 300 which may beused for implementing the inventive field-based similarity search systemand method according to the present invention; and

FIG. 28 illustrates a signal-bearing media 400 for storing instructionsfor performing the inventive field-based similarity search methodaccording to the present invention.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS OF THE INVENTION

Referring now to the drawings, FIG. 1 illustrates an inventive system100 for field-based similarity searching (e.g., three dimensionalsearching) databases (e.g., flexible molecule databases).

As shown in FIG. 1, the inventive field-based similarity search system100 includes a database 110 for storing at least one candidate molecule(e.g., a plurality of candidate molecules), an input device 120 (e.g., akeyboard or mouse) for inputting a query molecule, and a processor 130(e.g., microprocessor) for identifying a candidate molecule which issimilar to said query molecule based on a similarity of fragment pairfeatures.

Specifically, the processor 130 may be a central processing unit (CPU)or a plurality of processors. Further, the processor 130 may identify afeature of a query molecule fragment pair. The processor 130 may alsomatch a query molecule fragment pair feature with a candidate moleculefragment pair feature, and retrieve a candidate molecule fragment pairhaving at least a predetermined number of matching features. Further,the inventive system 100 may also include a memory device (e.g., RAM,ROM, etc.) for storing instructions for performing an operation usingthe processor 130. The memory device may also be used to store features,fragment pairs, matches of molecules, or any other data used orgenerated by the inventive system.

Further, inventive system 100 may also store specific algorithms in thememory device for performing a particular operation. The processor 130may, therefore, access the memory device and/or database in order toprocess data according to a particular algorithm stored therein. Forinstance, the processor 130 may access data stored in the memory deviceor database (e.g., plurality of databases) which pertains to a querymolecule or candidate molecule, in order to process such data and,therefore, determine is the candidate molecule is similar to the querymolecule.

Further, the processor 130 may align retrieved fragment pairs using apose clustering method. The processor 130 may also construct a fullyaligned candidate molecule by assembling retrieved fragment pairs. Theprocessor may also generate the fragment pair for the query molecule.

Further, the inventive system 100 may include a display device (e.g.,video display unit) for displaying, for example, the query molecule, acandidate molecule, or other data used or generated by the inventivesystem 100. Further, a user may utilize the display device in order tohelp the user direct an operation in the inventive system 100. Forinstance, the display device may be used with the input device 120 sothat the user may input instructions, data, etc. into the inventivesystem for storage in the database or memory device, and/or forprocessing by the processor 130.

An important feature of the inventive system 100 is that it allows theincorporation of context-specific information to balance considerationsin a manner suitable to the problem at hand. The result is that one-timecalibrations of similarity measures are inappropriate. Therefore, thebasis of a similarity search is tunable to the particular context beingconsidered.

In short, the present invention provides a systematic way of treatingfield-based similarity searching, without being confined to a particularfield definition. In other words, the present invention allows forfields ranging from simplistic, phenomenological fields, like theexamples discussed below, to fields derived from quantum mechanicalcalculations.

Overview

The inventive system 100 includes a database 110 which may include, forexample, a set of molecules over which to conduct a search. This set ofmolecules may be an explicitly defined set of molecules, or may be a“virtual” set of molecules (e.g., a set which is built from all or somecombination of smaller molecules according to specified rules.

For example, the database 110 may include a database of molecules, eachwith a single conformation, which is defined by a specification of itsatoms, bonds and atomic positions. Atom specification may be by element,a chemical tag denoting an atom in a certain environment, and/or an atomthat is to be treated in a certain way. Bond specification may involve areference to two atoms, and a bond type. Bond types can be a valancebond order, a chemical tag denoting the bond in a particularenvironment, and/or a bond that is to be treated in a certain way.

For a single conformation of the molecule to be specified, Cartesiancoordinates may be assigned to each atom. The co-ordinates can originatefrom x-ray crystal structure, nuclear magnetic resonance (NMR) solutionstructure, molecular mechanics, molecular dynamics, any form of quantummechanical or hybrid quantum/classical calculations, or an entirelyheuristical procedure.

Further, additional rules regarding how the molecules could combine tomake larger molecules may be added. For example, given two molecules Aand B, a rule may specify that A and B can combine to make C by a seriesof operations, such as alignment of atoms of A and B, addition ordeletion of atoms and/or bonds in A and/or B, and conformationadjustments to A, B, and/or C. In this case, the database 110 wouldinclude all or some of the possible C's that result from the applicationof a rule set comprised of any of the operations mentioned above.

Specifically, the inventive system 100 represents the conformationalspace for each molecule by a set of rules, rather than being explicitlydefined. This eliminates the intractable storage requirements thatexplicit enumeration requires for large sets of flexible molecules.

Specifically, each molecule may be partitioned into smaller fragments bythe selection (either manual or algorithmic) of a set of bonds tocleave. The allowed angles for a cleavage bond is enumerated explicitlyfor each pair of conformers in the corresponding node sets. Conformersof the fragments isolated by cleavage bonds, however, are explicitlyenumerated. A data representation in the form of a graph is constructedsuch that each node of this graph is a set of fragment conformers andeach edge of this graph is constructed such that each node of conformerof the molecule can then be expressed as a selection of one member ineach node set (fragment conformer) and edge set (cleavage bond angle).

Alternatively, the fragment sets of molecules may be left disconnectedin terms of a graph describing a larger molecule. A set of rules,likened to reaction descriptions, embodied as transformations such asadding or deleting atoms and/or bonds, and/or translating and/orrotating positions, can then be expressed in terms of matching topologyof a fragment, and thus need not refer to particular fragment sets, butany fragment set possessing one or more instances of the topology onwhich the transformations operate. The rules may then denote theresulting conformations of their application. The result of any suchapplication can itself by included in the pool of available fragmentsets for further application.

A key to the system 100 is that it avoids the need to search everyconformation of every molecule and apply a similarity metric to thequery at each possible alignment. This is done by using selectedfeatures from fragment pairs to align them to the query. Thus, unlikeprevious works (e.g., see U.S. Pat. No. 6,349,265 and U.S. Prov. patentapplication Ser. No. 09/275,568) the inventive system 100 uses fragmentpairs in place of the stored molecule. With said technology, featuresfrom the fragment pairs in the database may be matched with features ofthe query molecule.

Once features have been matched, the transformations used to align themmay be classified by said methodology. The transformations may begrouped together, for example, using a clustering procedure or a binningprocedure. A score may be assigned to the transformation groups based ongroup membership and/or other criteria based on the chemical and/orconformational similarity of the implied fragment pair alignment. Basedon this scoring criteria, one may select the best alignments of fragmentpairs to the query.

The user, therefore, has the option of combining the fragment pairs thathave been aligned to the query to create larger or complete molecules.For example, a user may be restricted to only suggesting molecules in agiven database. In this case, combining rules ensure that fragment pairsare not combined with others that do not share a common fragmentconformation. If partial structures are allowed, then after combinationsof fragment pairs are made, each product may be evaluated by applyingscoring criteria that qualifies candidates. Otherwise, candidatequalification criteria may be applied only to completely constructedstructures.

Alternatively, combinations of fragments according to reaction rules asdescribed above may be allowed. These fragments need not belong to thesame molecule. Combinations of fragment pairs may be directed byreaction rules, rather than the restriction of a common conformation.Each time a combination is made, the result may be checked for candidatequalification. Candidates may be stored, for example, in a database. Theresulting set of molecule conformers may also be ranked according to asimilarity metric.

Flexible Molecules

The inventive system 100 may represent the conformational space of aflexible molecule in terms of fragments and torsional angles of allowedconformations. A user definable property field may be used to computefeatures of fragment pairs. Features may be considered generalizationsof CoMMA descriptors that characterize local regions of the propertyfield by its local moments (B. D. Silverman and D. E. Platt, Comparativemolecular moment analysis (comma): 3d-qsar without molecularsuperposition, J. Med. Chem., 39:2129 2140, 1996). The features areinvariant under coordinate system transformations.

Features taken from a query molecule are used to form alignments withfragment pairs in the database. An assembly algorithm may then be usedto merge the fragment pairs into full structures, aligned to the query.Important to the system 100 is the use of a context adaptive descriptorscaling procedure as the basis for similarity. This helps to allow theuser to tune the weights of the various feature components based onexamples relevant to the particular context under investigation.

The property fields may range from simple, phenomenological fields, tofields derived from quantum mechanical calculations. For instance, theinventors have applied the inventive system 100 to adihydrofolate/methotrexate benchmark system, to show that when oneinjects relevant contextual information into the descriptor scalingprocedure, better results are obtained more efficiently.

Thus, the inventors have shown how the inventive system 100 provides foran effective and efficient search. For instance, the inventors haveprovided computer times for a query from a database that representsapproximately 23 million conformers of nine flexible molecules.

Conformational Space and Quantum Mechanical Calculations

Generally, the conformational space for drug-like molecules can becomequite appreciable. Some conventional methods represent theconformational space of a molecule as a collection of rigid fragmentswith preselected torsions (Gerhard Klebe and Thomas Mietzner, A fast andefficient method for generating biologically relevant conformations,Journal of Computer Aided Molecular Deisgn, 8:583-606, 1994). Otherapproaches prepare a database of representative conformations (Simon K.Kearsley, Dennis J. Underwood, Robert P. Sheridan, and Michael D.Miller, Flexibases: A way to enhance the use of molecular dockingmethods, Journal of Computer Aided Molecular Design, 8:565 582, 1994;Mathew Hahn, Three-dimensional shape-based searching of conformationallyflexible molecules, J. Chem. Inf. Comput. Sci., 37:80-86, 1996), orcompute conformations on the fly (Gareth Jones, Peter Willett, and RobinC. Glen, A genetic algorithm for flexible molecular overlay andpharmacophore elucidation, J. Comput.-Aided Mol. Des., 9:532-549, 1995).

The inventive system 100, on the other hand, is based on fragmentingmolecules into more manageable partitions. In particular, the inventivesystem 100 chooses as a smallest irreducible unit of characterization asthe fragment pair rather than the fragment. This treatment makesconformational space more manageable than conventional forms oftreatment.

Setting out to address flexible superposition via potentiallysophisticated property fields, one must give special attention toreducing the number of similarity evaluations that are to be performed,while maintaining some degree of confidence that the space has beencovered. The inventive system 100 attempts to pre-process as much aspossible, while still leaving enough tunability to adapt to the contextof the investigation. The system 100 seeks a practical tradeoff of thesize of conformational space, and the need for fragment pairs as largeas possible to maximize the relevance of the computer property fields.

More specifically, the inventive system 100 decomposes theconformational space of molecules to fragments. Then, to minimizeboundary effects, the system 100 computes the property field on pairs offragments. From the computer property fields of the fragment pairs,several features may be sampled and stored.

As noted briefly above, features may be considered to be generalizationsof CoMMA descriptors that characterize local regions of the propertyfield by its local moments. They are invariant under coordinate systemtransformations. To query the database for molecules that are similar toa particular molecule (e.g., the query molecule) features are calculatedfor the query molecule, and fragment pairs that contain a sufficientnumber of similar features are retrieved.

An important point is that, due to the coordinate system invariance ofthe features, the retrieval can happen without any alignment, oroptimization over rotational and translational degrees of freedom. Thealignment of retrieved fragment pairs on the query may be determined bya pose clustering procedure from the individual feature correspondences.Finally, to construct full aligned candidate molecules, the retrievedfragment pairs may be assembled by an incremental buildup procedure,similar in principle to ones used in docking (Matthias Rarey, BerudKramer, Thomas Lengauer, and Gerhard Klebe, A fast flexible dockingmethod using an incremental construction algorithm, J. Mol. Biol.,261:470 489, 1996)) and de novo design (Hans J. Bohm, The computerprogram ludi: A new method for the de novo design of enzyme inhibitors,J. Comput.-Aided. Mol. Des., 6:6178, 1992).

Fragment Pairs

There are two types of complexity in a database of three dimensionalmolecular structures: first, the conformational variety of individualmolecules, and second, in the case of a virtual combinatorial library,the combinatorial variety that results from the possibility ofsynthesizing a large number of different molecules from a small numberof reagents. Generally, the total number of three-dimensional structuresgrows exponentially both with the number of rotatable bonds and thenumber or reagents. Therefore, such a database should be efficientlyrepresented and stored.

A molecule can be partitioned into a fragment graph. This is an acyclicgraph that consists of fragment nodes connected by rotatable bond edges.Within a fragment node, there may be one zero, one or several rotatablebonds, as well as other degrees of freedom such as ring conformations.Given a molecule, there are in general multiple possible ways ofpartitioning it into a fragment graph. Typically, a fragment node mayconsist of about 10 heavy atoms, for example an aromatic ring plus somesubstituents.

FIG. 2 shows a sample partition. Specifically, FIG. 2 showsfragmentation and conformational expansion of methotrexate. As shownhere, single bonds may be sampled with a resolution of Δφ=60°, theaniline bond with Δφ=180°. Further, the molecule in FIG. 2 ispartitioned into three fragments.

Further, the substructure represented by a fragment node can in generalassume several different conformations. A specific conformation of afragment node may be referred to as a fragment. A fragment pair consistsof two neighboring fragments connected by a rotatable bond at a specificdihedral angle. A schematic representation of a fragment graph isdepicted in FIG. 3.

Fragment pairs are important entities in the inventive system 100.Property fields are defined and calculated on fragment pairs, and thesimilarity search is based on rotationally invariant features that arecalculated from those property fields. The assumption that underlies theuse of fragment pairs is that a property field calculated in theinterior of an isolated fragment pair is a good local approximation ofthe property field of the composite molecule.

Conceptually, the use of fragment pairs may be considered as equivalentto using overlapping fragments, with the overlap being about half theirsize. This has advantages both for the recognition and for the assemblysteps. First, the fragmentation locally distorts the property field inthose places where the molecule is cut. By using fragment pairs, theregions around the fragment joints are always in the interior of atleast one fragment pair, such that meaningful local descriptors can becalculated for them. Further, an aligned database molecule isconstructed by assembling fragment pairs that have one fragment incommon, and which both locally match the query with compatibleorientations. Thus, the relevant dihedral range of the connectingrotatable bonds determined (e.g. from steric and energetic criteria) isalready available in the pre-computed fragment pairs.

Obviously, this approach is suitable both for conventional moleculelibraries, as well as for virtual libraries supporting combinatorialchemistry approaches. The efficiency of the fragment pair representationis best discussed by way of an example. As indicated in FIG. 2, theconformational space of methorexate is spanned essentially by sixrotatable bonds. If five of the bonds are sampled in steps of 60°, andone bond is sampled at 180°, the total number of conformations isC _(MOL)=6⁵·2=15552.  (1)

In practice, fewer conformations have to be considered because some aresterically forbidden. Similar to equation (1), C_(FP1), the number offragment pairs from the lower and middle fragment node, and C_(FP2), thenumber of fragment pairs from the middle and upper fragment node areC _(FP1)=6·6·2=72, C _(FP2)=2·6·36=432.  (2)

The total number of fragment pairs is therefore 72+432=504. Furthermore,the size of a fragment pair is in this example only about ⅔ of the sizeof the whole molecule, with a corresponding smaller number of localdescriptors, so that the fragment pair representation needs about 50times less storage than the brute force enumeration.

More generally, for a molecule consisting of n fragments, each of whichhas C_(FRAG) conformations, and which are connected by rotational bondedges that are sampled in C_(RBE) steps, the total number ofconformation isC _(MOL) =C ^(M) _(FRAG) ·C ^(n−1) _(RBE),  (3)where n−1 is the number of rotatable bond edges. In comparison, thetotal number of fragment pairs isC _(FP)=(n−1)·C ² _(FRAG) ·C _(RBE).  (4)Note that equation (3) grows exponentially with n, whereas equation (4)only depends linearly on n.

The Property Field

A basis for the three dimensional similarity searching and alignment aretwo property fields μ({right arrow over (r)}) and ρ({right arrow over(r)}). The inventive system 100 makes no assumptions about these fields,except that μ({right arrow over (r)}) is scalar and positive. It mayalso be assumed that ρ({right arrow over (r)}) is a single scalar, butthis can be straightforwardly extended to multiple scalars, vectors ortensors.

Both fields μ({right arrow over (r)}) and ρ({right arrow over (r)}) areused to identify similar regions in query and database molecules. Theirgeometrical alignment however, is performed solely on the basis of fieldμ({right arrow over (r)}).

A simple-minded property field can be defined as:

$\begin{matrix}{{\mu( \overset{arrow}{r} )} = {{\frac{1}{( \sqrt{2\pi\;\sigma} )^{3}}{\sum\limits_{j = 1}^{N_{atoms}}\;{A_{j}\exp{\frac{- ( {\overset{arrow}{r} - {\overset{harpoonup}{a}}_{j}} )^{2}}{2\sigma^{2}}.{\rho( \overset{arrow}{r} )}}}}} = {{\mu( \overset{arrow}{r} )} - \overset{\_}{\mu}}}} & (5)\end{matrix}$Here the j-th atom is located at α_(j), and its electronegativity, A_(j)is given according to the Allred scale (Bodie E. Douglas, Darl H.McDaniel, and John Alexander, Concepts and Models of InorganicChemistry. John Wiley & Sons, 1983). The inventors used the followingvalues: A_(C)=2.6, A_(O)=3.4, A_(N)=3.0, A_(H)=2.2, A_(P)=2.2,A_(F)=4.0. σ is a parameter that controls the range of the Gaussiansmearing function. In their work, the inventors used a σ=0.5 Å. Therationale is to choose a value as big as possible, but small enough forthe property field not to be too uniform and unspecific. {right arrowover (μ)} is the average of μ({right arrow over (r)}) over all space.μ({right arrow over (r)}) is positive and ρ({right arrow over (r)}) isanalogous to a neutral charge distribution.

Another possible choice of a property field is

$\begin{matrix}{{{\mu( \overset{arrow}{r} )} = {\frac{1}{( \sqrt{2\pi\;\sigma} )^{3}}{\sum\limits_{j = 1}^{N_{atoms}}\;{M_{j}\exp\frac{- ( {\overset{arrow}{r} - {\overset{arrow}{a}}_{j}} )^{2}}{2\sigma^{2}}}}}}{{\rho( \overset{arrow}{r} )} = {\frac{1}{( \sqrt{2\pi\;\sigma} )^{3}}{\sum\limits_{j = 1}^{N_{atoms}}\;{Q_{j}\exp\frac{- ( {\overset{arrow}{r} - {\overset{harpoonup}{a}}_{j}} )^{2}}{2\sigma^{2}}}}}}} & (6)\end{matrix}$where M_(j) is the atomic mass and Q_(j) is the atomic charge computedby considering the “fraction of ionic character” of each bond in themolecule (M. Karplus and R. N. Porter, Atoms and Molecules, W. A.Benjamin, Inc., Menlo Park, Calif., 1971).

These example fields are by no means intended to offer new insight intoprocesses that underlie the chemistry of the present invention. Toexemplify and prototype the inventive system 100, the inventors selectedthe property field defined by equation (5) because of its simplicity. Inspite of its simplicity, however, when this property field is used, theinventive system 100 performs adequately, and thus may serve in thefuture as a base level, against which more elaborate fields may bebenchmarked.

Obviously, the choice of the property fields will have a great effectboth on the selectivity and on the efficiency of the search. The pointis that the preferred choice depends on the application and on thequestions asked. The exploration of different alternative fields isintended to be part of the process of adapting the inventive system 100to a certain domain.

Possible fields are by no means restricted to “smeared out” atomicproperties. The present invention may be intended to make use of fieldsderived from quantum mechanical calculations.

Descriptors and Feature Generation

Given the property fields μ({right arrow over (r)}) and ρ({right arrowover (x)}), the inventive system 100 may construct a set of local,rotationally invariant, moment-based descriptors. If the property fieldsof the query molecule and a database fragment pair are similar, thesedescriptors will have similar values. Since the descriptors arerotationally variant, no alignment is necessary, and the comparison canbe performed very quickly.

The similarity of the descriptors alone is an important but not asufficient criterion for the similarity of the fields. However, togetherwith the descriptors the inventive system 100 stores information ontheir relative positions and orientations within the query and databasestructures. When a database structure has enough descriptors similar tothe query, the relative positions and orientations of the descriptorsare compared. If these are also consistent, the two structures may beconsidered similar, and an approximate alignment is deduced from thisinformation.

Note that in order to obtain the alignment, no explicit (and costly)optimization of a property field overlap function with respect totranslation and rotation operators needs to be performed in theinventive system 100. However, if desired, such an optimization canafterwards be applied to a small set of promising candidates, startingfrom near-optimal initial conditions.

The first step in the construction of the descriptors is thepartitioning of the volume occupied by the structure into overlappingscoops. If the property fields are defined by smearing out atomicproperties A_(j), (as in the two examples set forth above), this may beperformed as follows: Let {{right arrow over (s)}_(k)} be a set ofpoints within or around the structure, such that the spheres with radiusR around these points provide a highly overlapping covering of therelevant regions of the property fields. Each of these spheres is calleda “scoop”. Further, define a ramping function

$\begin{matrix}{{\Delta(a)} = \{ \begin{matrix}1 & {a \leq R} \\{0 - {a/R}} & {a > R}\end{matrix} } & (7)\end{matrix}$and a window function

$\begin{matrix}{{h(r)} = \{ \begin{matrix}1 & {r \leq R} \\0 & {r > R}\end{matrix} } & (8)\end{matrix}$Therefore, the “attenuated atomic properties” that contribute to thek-th scoop may, therefore, be given byA _(j) ^((k))=Δ(|{right arrow over (a)} _(j) −{right arrow over (s)}_(k)|)·A _(j)   (9)and the k-th scoop's property field is

$\begin{matrix}{{\mu_{k}( \overset{arrow}{r} )} = {{{h( {{\overset{arrow}{r} - {\overset{arrow}{s}}_{k}}} )} \cdot \frac{1}{( \sqrt{2{\pi\sigma}} )^{3}}}{\sum\limits_{j}^{N_{atoms}}\;{A_{j}^{(k)}\exp\frac{- ( {\overset{arrow}{r} - {\overset{arrow}{a}}_{j}} )^{2}}{2\sigma^{2}}}}}} & (10)\end{matrix}$and corresponding for ρ_(k)({right arrow over (r)}), as in equation (5).The intention of the ramping function (7) is that the property fieldsμ_(k) and ρ_(k) (and therefore the descriptors) are continuous functionsof the location of the scoop center {right arrow over (s)}_(k).

For general property fields μ({right arrow over (r)}) and ρ({right arrowover (r)}) that are not obtained by smearing out atomic properties,scoop property fields can simply be obtained by settingμ_(k)({right arrow over (r)})=h(|{right arrow over (r)}−{right arrowover (s)} _(k)|)·μ({right arrow over (r)}),  (11)and correspondingly for ρ({right arrow over (r)}).

For example, the set of points {{right arrow over (s)}_(k)} may be theset of all atom positions, and R=3 Å. With this, the scoops may objectsof intermediate size, larger than a functional group, but smaller than afragment pair. Typically, a scoop may contain 6 to 8 non-hydrogen atoms.

Having defined a set of scoops and their associated local propertyfields μ_(k) and ρ_(k), rotationally invariant descriptors may beconstructed. There will be a descriptor consisting of 16 real numbersfor each scoop. To simplify the notation, in the following, the index kthat numbers the scoops was dropped, and the continuum fields wasreplaced by the discretized versions μ_(i) and ρ_(i) defined on a gridof points {{right arrow over (r)}_(i)|i=1, . . . N}. For the grid, aface-centered cubic lattice (other types of lattices can also be used)of unit cell length ΔR=R/18 within each scoop of radius R has been used.Further, the grid spacing ΔR has been determined by varying the gridorientation with respect to the atoms in the scoop, and making sure thatthe resulting descriptors, as described below, do not significantlydepend on the orientation.

The zeroth moments of the fields are

$\begin{matrix}{{M = {\sum\limits_{i = 1}^{N}\;\mu_{i}}},{Q = {\sum\limits_{i = {1\,}}^{N}\;\rho_{i}}}} & (12)\end{matrix}$In the case of the property field defined by equation (6), M and Qcorrespond to total mass and total charge within the scoop.

The center of the μ-field is defined by

$\begin{matrix}{{\overset{arrow}{c}}_{\mu} = {\frac{1}{M}{\sum\limits_{i = 1}^{N}\;{\mu_{i}{\overset{arrow}{r}}_{i}}}}} & (13)\end{matrix}$and the center of the ρ field by

$\begin{matrix}{{\overset{arrow}{c}}_{\rho} = \{ \begin{matrix}{\frac{1}{Q}\overset{arrow}{b}} & {{{if}\mspace{14mu}{Q}} > ɛ_{Q}} \\{\frac{1}{3b^{2}}( {{B\;\overset{arrow}{b}} - {\frac{{\overset{arrow}{b}}^{t}B\;\overset{arrow}{b}}{4b^{2}}\overset{arrow}{b}}} )} & {otherwise}\end{matrix} } & (14)\end{matrix}$where {right arrow over (b)} and B are dipole and quadrupole moment ofthe ρ-field with respect to the origin of the laboratory coordinatesystem,

$\begin{matrix}{{\overset{arrow}{b} = {\sum\limits_{i = 1}^{N}\;{\rho_{i}{\overset{arrow}{r}}_{i}}}}{B = {\sum\limits_{i = 1}^{N}\;{\rho_{i}( {{3{\overset{arrow}{r}}_{i}{\overset{arrow}{r}}_{i}^{t}} - {r_{i}^{2}11}} )}}}} & (15)\end{matrix}$and the superscript t stands for transposition. In the case of theproperty field defined by equation (6), {right arrow over (C)}_(μ)is thecenter of mass, and the first line of equation (14) is the center ofcharge. The center of charge may be defined only if the scoop has a netcharge (e.g., if the charge is larger than the threshold ε_(Q).Otherwise, the second line of equation (14) calculates the center ofdipole.

The inertial tensor J and a cubic vector {right arrow over (J)} withrespect to {right arrow over (C)}_(μ), the center of μ, are defined as

$\begin{matrix}{J = {\sum\limits_{i = 1}^{N}\;{\mu_{i}( {{r_{i}^{\prime\; 2}11} - {{\overset{arrow}{r}}_{i}^{\prime}{\overset{arrow}{r}}_{i}^{\prime\; t}}} )}}} & (16) \\{\overset{arrow}{j} = {\sum\limits_{i = 1}^{N}\;{\mu_{i}r_{i}^{\prime\; 2}{\overset{arrow}{r}}_{i}^{\prime}}}} & (17)\end{matrix}$where {right arrow over (r)}_(i)′={right arrow over (r)}_(i)−{rightarrow over (C)}_(μ). Similarly, dipole moment {right arrow over (p)} andquadrupole moment Q of the ρ-field with respect to {right arrow over(C)}_(ρ), the center of ρ, may be defined as follows:

$\begin{matrix}{\overset{arrow}{p} = {\sum\limits_{i = 1}^{N}\;{\rho_{i}{\overset{arrow}{r}}_{i}^{''}}}} & (18) \\{Q = {\sum\limits_{i = 1}^{N}\;{\rho_{i}( {{3{\overset{arrow}{r}}_{i}^{''}{\overset{arrow}{r}}_{i}^{''\; t}} - {r_{i}^{''\; 2}11}} )}}} & (19)\end{matrix}$where {right arrow over (r)}_(i)″={right arrow over (r)}_(i)−{rightarrow over (C)}_(ρ).

It is important to note that the quantities (e.g., equations) (17)-(19)are expressed in a uniquely defined scoop-internal coordinate system sothat they no longer depend on the arbitrary choice of the laboratoryframe. Therefore, the descriptors of different scoops can be comparedwithout prior alignment. The axes of the scoop internal coordinatesystem are given by the eigenvectors of the inertial tensor J:J{right arrow over (v)} _(n) =J _(n) {right arrow over (v)} _(n) , n=1,2, 3.  (20)

The positive numbers J_(n) are the inertial moments. The vectors {rightarrow over (v)}_(n) can be arranged into the columns of ad orthonormalmatrix V. An arbitrary vector may be then transformed from thelaboratory frame to the internal frame by left-multiplying it withV^(t).

In order to uniquely define the internal coordinate system, (i) theordering, and (ii) the sensing (i.e. the signs) of the coordinate axesshould be fixed.

The ordering is defined by J₁≦J₂≦J₃. If two or three of the eigenvaluesof J are degenerate, then there are no unique eigenvectors, but rathertwo- or three-dimensional eigenspaces, there is no well-defined inertialcoordinate system, and the corresponding scoop is not used to generate adescriptor. Degeneracy in this context means that two eigenvalues areequal to within some threshold that may depend on the choice of propertyfield. The degeneracy condition isJ ₂ /J ₁<1+ε_(J) or J ₃ /J ₂<1+ε_(J).  (21)To fix the sensing, the dimensionless asymmetry vector was defined by

$\begin{matrix}{\overset{arrow}{\alpha} = {\begin{pmatrix}{RJ}_{1} & 0 & 0 \\0 & {RJ}_{2} & 0 \\0 & 0 & {RJ}_{3}\end{pmatrix}^{- 1}V^{t}\overset{arrow}{j}}} & (22)\end{matrix}$where {right arrow over (J)} is the cubic vector from equation (17), andthe signs of the axes were selected according to Table I illustrated inFIG. 4.

The sign s ε{−1, 1} is determined by requiring right-handedness, i.e.det V=1. The table above represents a unique choice of the axes sensingdepending only on the cubic vector {right arrow over (J)}.

If two, or three components of α are within some chosen threshold ofzero, one is left with two or even four different equally admissiblechoices for the axes sensing. For descriptors stored in the database, anarbitrary choice may simply be taken. For the query features that are tobe matched against the database, a descriptor is generated for eachadmissible choice of axes sensing. For the present data, the inventorsused the duplication condition α_(n)/RJ_(n)<0.02.

As a result, the CoMMA descriptor X_(k) for the k-th scoop, which may becalled a feature, may consist of the d=16 real numbers which are shownin Table II in FIG. 5.

If the ρ field is more complex than a scalar field (e.g., a combinationof several scalars) or a vector or a tensor field, then the first andsecond moments {right arrow over (p)} and Q will have a correspondinglygreater number of components, and d, the number of components of thedescriptor X_(k) is larger than 16.

Since the vector and tensor quantities in the descriptor are expressedin the internal coordinate system, which only depends on localproperties of the molecule, the descriptor is completely independent ofthe laboratory frame. This has two important implications: first, twoscoop descriptors can be compared against each other without prioralignment, and second, if two descriptors are found to be similar, thetwo corresponding molecules can be locally aligned by simply overlayingthe internal coordinate systems of the two scoops.

Descriptor Scaling and Quantization

The scoop descriptors X_(k)=(X_(k1), . . . , X_(kd)) cannot be usedstraightforwardly to define similarity between scoops because thecomponents X_(k1), X_(k2), . . . have different physical units, andbecause the different components may be more or less important for thesimilarity search at hand. For example, it may be important in aparticular application of this method to recognize and distinguishbetween some specific set of structural motifs or chemical functionalgroups in identifying fragment pairs from a database to align on a querymolecule. In a different application of the inventive system 100, it maybe more important instead to recognize and distinguish a different setof motifs, or regions of electrical polarity. Clearly, a useful systemshould be able to adapt to what is meaningful to the user in assessingsimilarity.

The inventors, therefore, defined a distance measure that weights thedifferent descriptors according to their importance as perceived from atraining set of descriptors. The training data consists of a number ofsample descriptors that are categorized into groups. From this, theinventive system 100 may “learn” two types of descriptor variations:Important variations may be considered those that occur systematicallybetween descriptors from different groups. Such variations may be usedto define the distance measure. The descriptors within a group areconsidered similar, and the distance measure is made to ignore thesetypes of variations.

While there is a vast repertoire of methods from the disciplines ofclassification and pattern recognition to address this task, theinventive system 100 may simply use Fisher's linear discriminantanalysis. It provides a linear mapping from the d-dimensional descriptorspace into a lower-dimensional space:Y_(k)=W^(t)X^(k)   (23)where W is a d×p matrix with p≦d.

The discriminant matrix W is calculated from the user-suppliedclassification of a sample of descriptors X_(k), into p+1 groups. Thewithin-group scatter matrix S_(w) is the average covariance matrix ofdescriptors that are in the same group, and the between-group scattermatrix S_(b) is the covariance of the group centroids (Richard O. Dudaand Peter E. Hart, Pattern Classification and Scene Analysis, John Wiley& Sons, Inc., New York, 1973). The discriminant matrix W is definedthrough the maximization of the criterion function:

$\begin{matrix}{{J(W)} = {\frac{{W^{t}S_{b}W}}{{W^{t}S_{w}W}}.}} & (24)\end{matrix}$This optimization criterion selects W such that the distances betweenthe Y_(k) within the same group are minimized, whereas the distancesbetween the groups' centroids are maximized. Numerically, W may becalculated using a generalized eigenvalue routine (IBM, Poughkeepsie,N.Y. Engineering and Scientific Subroutine Library for AIX, Version 3,Guide and Reference, 1997).

To allow for a fast database lookup of stored descriptors that aresimilar to a query, descriptor space may be quantized. Descriptors thatfall within the same compartment may be considered similar, and arematched. Those that fall into different compartments do not match.

For example, the compartments may be defined by a rectilinear grid indiscriminant space (i.e. in the space of the Y_(k)). The grid spacingss_(j) are chosen such that a grid cell can accommodate the typicalscatter within a group. This is done by a heuristic that sets the binwidth s_(j) to four times the largest standard deviation of the j-thcomponent (j=1, . . . , p) within an individual group, and the right endof the leftmost bin to the minimum over all groups.

For example, FIG. 6 illustrates a sample distribution of features indiscriminant space. Specifically, FIG. 6 shows the distribution offeatures after mapping into a 2-D space by way of discriminant analysis,with the functional grouping. The features marked with diamonds,triangles and circles represent the three groups. The remaining featuresare marked with plus symbols. The query is represented by 53 features,and a single conformation of the database molecule (the crystallographicone) is represented by 56 features.

Although the scaling and quantization in the inventive system 100 may befairly simple, it is robust. Moreover, the inventive system 100 doesaccomplish a context-adapted descriptor calibration and similaritymeasure, utilizing a user-defined training set of descriptors. Missedmatches as a consequence of cell boundaries are not as likely in the lowdimension in which the grid is defined as they would be forhigher-dimensional situations. Since there is redundancy in the set ofscoops characterizing a molecule, a meaningful alignment will berecovered if just a fraction of them are actually matched.

A virtue of linear mappings (e.g., equation (23)), in comparison to, forexample, neural networks, is that linear mappings have a limited numberof parameters and require only a relatively small training set, which isimportant for practical applications. Furthermore, the mapping (e.g.,equation (23)) and the subsequent discretization are exactly invariantunder overall linear transforma-tions of the descriptors. This meansthat the calibration and quantization scheme does not depend on whether,for example, length is measured in meters or Angstroms, and mass ingrams or amu.

The training set may be chosen according to the following criteria: thedifferent groups should be selected to contain examples of structural orfunctional units that are relevant for the similarity search. Within theindividual groups, members should represent the kinds of variations thatoccur in the descriptor database, like experimental uncertainty in bondlengths and angles, different environments of functional groups, anddifferent conformations deemed irrelevant for the problem at hand.

The Feature Database

The previous section generated a context-adapted mapping from descriptorspace to an integer set of feature keys. These keys are simply theindices that label the cells in discriminant space. The use of a hashtable and fast integer key lookup methods supports efficient queriesagainst large databases, with access times largely independent ofdatabase size.

In principle, compared to a method that would use a detailed, fullycontinuous distance metric, the quantization of the descriptors toproduce the keys causes a loss of sensitivity (more false negatives),and a loss of selectivity (more false positives) in the similaritysearch. However, the set of descriptors that describe a molecule may behighly redundant, so that an incomplete set of scoop matches still leadsto a complete alignment of the molecules. Furthermore, false positivematches are reduced in a subsequent clustering step since false positivematches do not occur consistently.

The feature database may be the product of two inputs: a set ofdescriptors, generated from all conformations of a selection of fragmentgraphs, and the context-adapted descriptor-to-key mapping. The featuredatabase is a hash table, whose keys are given by evaluating the mappingon the descriptors. An entry in the hash table consists of a referenceback to a fragment pair, and a description of the internal frameassociated with the descriptor. The explicit values of the descriptorsare not stored in the feature database. The thrifty use of memory by thefeature database is important for the scalability of the inventivesystem 100.

Generally, the calculation of the descriptor set for all the fragmentpairs of the fragment graphs may be an expensive part of the inventivesystem 100. However, the descriptor set may be computed only one time,in a preprocessing step, and then the set may be stored. Application ofthe descriptor to key mapping is fairly cheap and quick. As the domaincontext is varied, the descriptor-to-key mapping will change, anddifferent feature databases can be created to query against. Finally, agiven feature database can be queried very rapidly from the keys ofquery features, with any number of queries, including differingconformations of the same molecule, as well as differing molecules.

Feature Correspondence

The feature database may be used to align fragment pairs to the querymolecule. The basic idea is to calculate scoops, descriptors, and keysfor the query in the same way as for the fragment pairs stored in thedatabase. Each query key then accesses the matching entries in thefeature database. Each pair of query and database scoops that have thesame key may be referred to as a correspondence.

By overlaying the internal coordinate axes of such a scoop pair, eachcorrespondence implies a certain alignment of a stored fragment paironto the query. Whereas such a single correspondence might becoincidental, a significant alignment—what may be referred to as ahypothesis—is inferred when several independent correspondences fromdifferent regions of the query and fragment pair support the samerelative orientation of the two. This assumption is a basis ofpose-clustering methods (G. Stockman, Object recognition andlocalization via pose clustering, Computer Vision, Graphics, and ImageProcessing, 40:361387, 1987). A selected number of the strongesthypotheses may be passed on to the assembly.

The feature correspondence process may, therefore, include constructionof all correspondences by keyed access from the query to the featuredatabase, clustering of the correspondences, and construction of thehypotheses as average alignments of the significant clusters.

The internal coordinate system that is associated with a feature may bespecified by its origin {right arrow over (C)}_(μ), and an orthonormalsystem of inertial eigenvectors V (e.g., see equations (13) and (20)).The transformation of laboratory frame coordinates {right arrow over(x)} into internal coordinates may be given byT:{right arrow over (x)}

V ^(t)({right arrow over (x)}−{right arrow over (c)} _(μ)).  (25)Given a correspondence between a query feature X_(q) and a storedfeature X_(s), and the two associated transformations T_(q) and T_(s),the transformation that aligns the stored fragment pair coordinates ontothe query isT _(qs) =T ⁻¹ _(q) oT _(s) :{right arrow over (x)}

{right arrow over (c)} _(μ,q) +V _(q) V _(s) ¹({right arrow over(x)}−{right arrow over (c)} _(μ,s)).  (26)This is a putative alignment of the fragment pair represented in thedatabase onto the query molecule, based on a single featurecorrespondence.

However, it would be impractical and prohibitively expensive to evaluateand score each such alignment separately. In the inventive system 100,therefore, the set of all putative alignments may be divided intoclusters. In order to perform clustering, a metric in the space oftransformations (e.g., see equation (26)) may be required. For example,the inventors have used the following metric:d(T _(qs) , T _(q′s′))=|T _(qs)({right arrow over (x)} ₀)−T_(q′s′)({right arrow over (x)}₀)|+2α tan(1/2d _(rot))   (27)d _(rot)=α cos(1/2(Tr{V _(q′) V ^(t) _(s′) V _(s) V ^(t) _(q)}−1))  (28)if s and s′ are from the same fragment pair, and d(T_(qs), T_(q′s′))=∞if they are from different fragment pairs. {right arrow over (x)}₀ isthe center of geometry of the fragment pair coordinates, and the firstterm on the right hand side of equation (27) is simply the Euclideandistance between the transformed fragment pair centers. V_(q′)V^(t)_(s′)V_(s) V^(t) _(q) is the rotation part of the transformationT_(q′s′) o T⁻¹ _(qs) that maps a set of coordinates transformed byT_(qs) onto the one transformed by T_(q′s′), and d_(rot) is themagnitude of the angle of that rotation.

Further, the function

${f(x)} = {2\mspace{11mu}\tan\mspace{11mu}\frac{x}{2}}$is close to the identity for small angles, but becomes large when x goestowards π. This function may be used to make sure that transformationswith very different rotations are considered very far apart. Theparameter α provides a measure of the relative weighting of orientationand translation for the transformation distance. For example, α=3 Å maybe selected for all fragment pairs.

Having defined a metric, the clustering may be performed. For example,the hierarchical clustering method G03ECF implemented in the NAG library(NAG Ltd., Oxford, UK. The NAG Fortran Library Manual, Mark 16, 1993),with the complete-linkage distance updating method, may be used.Hierarchical clustering may be selected over partitional, because thelatter is cumbersome for non-Euclidean metrics like equation (27), andthe complete-linkage method because it produces the most compactclusters, which is desirable for the subsequent averaging (Anil K. Jainand Richard C. Dubes, Algorithm for Clustering Data, Prentice Hall,1988).

The only parameter of the clustering step may be the distance leveld_(clust) at which the dendrogram is cut. For instance, after someinvestigation (e.g., the choice for d_(clust) used in the present workwas made based on a number of experiments with the DHF-MTX system.However, results were relatively insensitive to values in the range of2.5 to 4.0 Å. This value is probably appropriate for studies using thesame clustering algorithm, transformation distance metric, withfragments that are approximately 10 heavy atoms in size, and for nuclearplacement of scoops) the inventors have used d_(clust)=3 Å. Note that ifd_(clust) is too large, what should be distinct clusters will be mergedand the average transformation will not be representative of anytransformation of these distinct clusters. On the other hand, ifd_(clust) is too small, the number of members in each cluster is smalland no clusters emerge with sufficient signal.

For hypothesis building, the largest and therefore most significantclusters may be selected, and average transformations calculated. Forinstance, consider a cluster of n transformations T₁, . . . T_(n), eachone represented byT _(i) :{right arrow over (x)}

{right arrow over (t)} _(i) +R _(i) {right arrow over (x)}, i=1, . . . ,n.  (29)

Representations given by equations (29) and (26) are related byR=V_(q)V_(s) ^(t) and {right arrow over (t)}={right arrow over(c)}_(μ,q)−R{right arrow over (c)}_(μ,s). The average rotation may becalculated as

$\begin{matrix}{{{R_{av} = {UW}},{where}}{{UDW} = {\sum\limits_{i = 1}^{N}\; R_{i}}}} & (30)\end{matrix}$is a singular value decomposition (SVD) of Σ_(i)R_(i) (W. Dan Curtis,Adam L. Janin, and Karel Zikan, A note on averaging rotations, In IEEEVirtual Reality Annual International Symposium, pages 377-385, IEEE,1993).

This is well-defined as long as the rotations in the cluster are not toodifferent. In the situation where rotations vary widely, the notionitself of an average rotation becomes disputable. The averagetranslation vector {right arrow over (t)}_(av) is calculated byrequiring that the fragment pair center {right arrow over (x)}₀ underthe average transformation is the arithmetic average of the fragmentpair center under the individual transformations in the cluster,

$\begin{matrix}{{\overset{arrow}{t}}_{av} = {{\frac{1}{2}\lbrack {{\sum\limits_{i = 1}^{n}\;{\overset{arrow}{t}}_{i}} + {R_{i}{\overset{arrow}{x}}_{0}}} \rbrack} - {R_{av}{{\overset{arrow}{x}}_{0}.}}}} & (31)\end{matrix}$The average transformation for the cluster may be therefore T:{rightarrow over (x)}

{right arrow over (t)}_(av) 30 R_(av){right arrow over (x)}. Forexample, all feature correspondences may carry an equal weight both inthe clustering and averaging steps. Alternatively, it may be consideredthat some correspondences are more significant than others.

Summing up, for each query feature, the descriptor-to-key mapping mayform a correspondence with all stored features that have the same keyvalue. The set of all such pairs may be clustered according to themetric in transformation space. There might be correspondences involvingmany different stored fragment pairs, but the correspondences within onecluster may only refer to the same fragment pair.

Further, the largest clusters, according to a user-defined minimumcluster size n_(clust) may be selected. For each cluster, the averagetransformation may be calculated and applied to the coordinate of thefragment pair from whose features it was derived. The result is a set ofhypotheses, that is, fragment pairs aligned on the query.

Assembly

The assembly process in the inventive system 100 may begin with this setof hypotheses: fragment pairs positioned in the query frame according tothe transformations derived in the clustering procedure. These fragmentpairs may belong to any molecule in the database. An objective is tomerge these fragment pairs into complete, aligned structures. Theassembly algorithm should be able to process as much in parallel aspossible.

If only fragment pairs belonging to the same fragment graph are allowedto be merged, the structures that result from the assembly process willbe conformers of those molecules that were used to build the database.However, if fragment pairs from different fragment graphs are allowed tomerge, new structures may be created through the assembly. Furthermore,pieces of larger structures may qualify as matches to the query.

The assembly may be an iterative process, where each iteration stepbegins with a set of fragment pairs and/or partially assembledstructures, and produces a set of partially or fully assembledstructures that have increased in size by one fragment. Whereas theoverall iteration loop runs sequentially, within a step, many fragmentpairs or partial structures can be processed in parallel.

At the beginning of each step, fragment pairs and any partial structuresfrom previous steps may be grouped together and referred to as bases. Inother words, a base may be a group of adjacent fragments, that have beenaligned to the query, and connected with specific torsional angles ofthe rotatable bonds. All atom coordinates may be expressed in the queryframe. In addition, a base carries a record of which fragment nodes itcontains, and which fragment pairs could be used to grow it.

The first phase of an assembly step may be termed the base expansionphase. In this phase, the list of potential merges of fragment pairswith bases may be determined. It results from consideration of thefronts of the growing bases. The front of a base is defined as the setof rotatable bond edges between a matched and an unmatched fragment nodeon the fragment graph. Any fragment pair from the set of hypotheses thatincludes both a frontal rotatable bond edge and matches the fragmentconformer present in the base can potentially merge with the base. Amerge between a base and fragment pair may occur if the root mean squaredistance computed between corresponding atoms in the fragments that arecommon to the base and the fragment pair is less than a threshold. Notethat during the assembly process a hypothesis fragment pair can be usedfor merges many times, onto multiple growing bases.

There are different ways to merge a base and a fragment pair that haveclose, but not identical atom positions of the common fragment. First,one could leave the base fixed and superpose the fragment pair onto thebase's fragment. In the other extreme, one could leave the fragment pairfixed and superpose the base onto the fragment in the fragment pair.

However, the inventors have used an intermediate option, which isconstructed by joining the base and the fragment pair, and thendetermining the least squares alignment (K. S. Arun, T. S. Huang, and S.D. Blostein, Least square fitting of two 3-d point sets, IEEETransactions on Pattern Analysis and Machine Intelligence, PAMI-9(5):698700, 1987) of the unique corresponding atoms in the original base andthe grown one, and in the fragment pair and the grown base. The atoms ofthe common fragment are not necessarily included in this calculation.Note, that due to the merging, the orientation and position of a basedepends not only on the fragment pairs that went into it, but also onthe order in which they were merged. Therefore, multiple identical basescan be produced with slightly different positions and orientationsrelative to the query molecule.

After each merge, a bump check may be performed, which checks whetheratoms from the newly added fragment are too close to those that were inthe base before. For instance, the inventors have used a threshold of1.7 Å for non-bonded atom-atom distance (e.g., the value of 1.7 Å chosenfor the bump check parameters used in this work is rather small.Therefore, some high energy conformations are used as fragment pairs andalso some high energy candidates are produced during assembly. The valuewas chosen to screen out only the worst cases of steric overlap in orderto assess the method with a larger work load. The performance of themethod improves if this parameter is increased).

After a bump check, a shape screen may be applied, which prevents thebase from growing too far outside the query's volume. The screen may beperformed simply by verifying that no atom in the base is more than athreshold distance from the closest atom in the query. For instance,this threshold may default to 3.5 Å.

Bases that pass the shape screen may be then scored against the query.For example, the default scoring function may be a simple Carbofunction, as used in other work (R. Carbo, L. Leyda, and M. Arnaua, Howsimilar is a molecule to another? An electron density measure ofsimilarity between two molecular structures, Int. J. Quant. Chem.,17:1185, 1189, 1980).

$\begin{matrix}{{Q = {\frac{1}{N_{q}}{\int_{R^{3}}^{\;}{( {\sum\limits_{j = 1}^{N_{q}}\;{h( {\overset{arrow}{x} - {\overset{arrow}{a}}_{j}} )}} )( {\sum\limits_{j = 1}^{\; N_{b}}\;{h( {\overset{arrow}{x} - {\overset{arrow}{b}}_{j}} )}} ){\mathbb{d}^{3}\overset{arrow}{x}}}}}},} & (32)\end{matrix}$where {right arrow over (a)}_(j) is the atom coordinate of the j^(th)query atom, {right arrow over (b)}_(j) is the atom coordinate of thej^(th) atom in the base, and h({right arrow over (x)})=π^(−3/4)τ^(−3/2)exp(−x²/2τ²) is a normalized three dimensional Gaussian density with τ=1Å. N_(q) and N_(b) are the numbers of atoms in the query molecule andthe base, respectively. Scoring functions can vary widely in theirsophistication (Andrew C. Good and W. Graham Richards, Explicitcalculation of 3d molecular similarity, In Hugo Kubinyi, Gerd Folkers,and Yvonne C. Martin, editors, 3D QSAR in Drug Design, volume 2, pages321-338, Kluwer Academic Publishers, Great Britain, 1996). The inventorshave chosen equation (32) for its simplicity.

A base that passes certain criteria may qualify as a candidate, meaningthat it may be considered a successful match to the query. For instance,a base may be considered a candidate if it has some minimum number offragments, passes all applicable checks and/or has a sufficient scorewith respect to the scoring function in use.

Bases that have no opportunities for growth may be removed fromconsideration in subsequent iterations of the assembly process. Thebases remaining may be used as input to the next iteration of theassembly phase. The assembly process may be terminated when there are nobases left for consideration (e.g., when there are no bases left togrow).

Note that the procedure may be considered exhaustive in that allcandidate alignments may be produced if they qualify with respect to thebump check, shape screen and scoring criteria. The inventive system 100may, therefore, attempt to produce the better candidates early. Forexample, in their application of the inventive system 100 discussedbelow, the inventors produced all possible qualifying candidatealignments that could be constructed from the aligned fragment pairssubmitted to the assembly phase.

Example: Application of the Present Invention to Dihydrofolate andMethotrexate

For example, the inventors have applied the inventive system 100 to thecase of dihydrofolate (DHF) and methotrexate (MTX). This case has beenthe subject of study for numerous methods of superposition (Michael D.Miller, Robert P. Sheridan, and Simon K. Kearsley, Sq: A program forrapidly producing pharmacophorically relevent molecular superpositions,J. Med. Chem., 42:1505-1514, 1999; Christian Lemmen and Thomas Lengauer,Time-efficient flexible superposition of medium-sized molecules, Journalof Computer-Aided Molecular Design, 11:357 368, 1997; Simon K. Kearsleyand Graham M. Smith, An alternative method for the alignment ofmolecular structures: maximizing electrostatic and steric overlap,Journal of Computer Aided Molecular Design, 8:565 582, 1994) as well asdocking (Matthias Rarey, Berud Kramer, Thomas Lengauer, and GerhardKlebe, A fast flexible docking method using an incremental constructionalgorithm, J. Mol. Biol., 261:470 489, 1996; David M. Lorber and BrianK. Shoichet, Flexible ligand docking using conformational ensembles,Protein Science, 7:938 950, 1998). In fact, the case has become abenchmark for such methods, as it exhibits an interesting aspect thatthe most reasonable superposition from the perspective of topology isdifferent from the superposition that can be deduced from aligning theenzyme parts of the crystal structures of ligand-enzyme complexes of DHFand MTX bound to dihydrofolate reductase (DHFR) (Gerhard Klebe.Structural alignment of molecules, In Hugo Kubinyi, editor, 3D QSAR inDrug Design, pages 173-199, ESCOM, Leiden, 1993).

The latter superposition can be understood in terms of electrostaticsand hydrogen bonding sites (Hugo Kubinyi, Similarity and dissimilarity:A medicinal chemist's view, In Hugo Kubinyi, Gerd Folkers, and Yvonne C.Martin, editors, 3D QSAR in Drug Design, volume 3, pages 317-338.Kluwer, Dordrecht/Boston/London, 1998). The MTX-DHF system may thusserve as a probe to characterize how such methods weight the importanceof topological similarity, electrostatic similarity, and potentialnon-bonded interactions. The inventors chose this case as their casestudy to characterize how the inventive system 100 performs, using thevery simply property field detailed above.

To this end, the inventors described two experiments, which illustratethe importance of feature classification. The first considers thealignment of a rigid conformation of MTX on a rigid conformation of DHF.Both conformations are extracted from the crystal structures of themolecules bound to DHFR. Features are computed at atom centers andgrouped according to a classification scheme derived with knowledge ofthe respective binding modes observed in the crystal structures. Thisfunctional-based grouping (e.g., as shown in FIGS. 7(A) and 7(B)) iscompared to the case where all features are classified equally, andevery query feature is compared to every stored feature.

For example, FIGS. 7(A) and 7(B) show the definition of the three groupsfor the descriptor scaling. The first group may consist of thedescriptors derived from scoops around the guanidine of the pteridinesystem. There are four such scoops for DHF, and four for MTX. Therefore,the first group consists of 8 descriptors. Similarly, the second groupis made up of 8 descriptors from the chain linking the pteridine andbenzamide rings, and the third group of 16 descriptors from around thep-amino-benzamide ring.

Taking DHF as the query, MTX may be aligned, for example, under the twoconditions of classification, and the results compared. It should benoted that knowledge of the particular binding mode is not a requirementfor application of the inventive system 100. If, however, one has suchinformation, one should be able to use it to better characterize themeaning of similarity in a similarity search.

As a second experiment the inventors used DHF as a query molecule on adatabase that represents the full conformational space of MTX. Thefeatures were classified using two schemes. The first scheme is thefunctional-based grouping described above. The second scheme assumes noknowledge of the binding modes and simply groups features by the elementtype (e.g., C, N, or O) of the central atom.

Comparison of the results of using these two schemes illustrates thevalue of injecting relevant context into the feature classificationscheme. The inventors compared the workload consequent from these twofeature classification schemes, and concluded with the top scoringalignments assembled from the fragment pairs of MTX. As noted below,reasonable results are obtained with both grouping schemes. However,when features are classified with the functional-based (i.e.,context-derived) scheme, the results are obtained more efficiently andare of higher quality, as assessed by the Carbo scoring function or byvisual inspection.

Rigid Body Superposition

Structures of DHF and MTX were extracted from the crystal structureswith PDB identifiers 1dhf and 4dfr respectively. 1dhf provides thecoordinates of DHF bound to the human form of the enzyme DHFR (N. J.Prendergast, T. J. DeCamp, P. L. Smith, and J. H. Fresheim, Expressionand site-directed mutagenesis of human dihydrogolate reductase,Biochemistry, 27:3664, 1988). 4dfr provides the coordinates of MTX boundto an E. coli strain (J. T. Bolin, D. J. Filman, D. A. Matthew, R. C.Hamlin, and J. Kraut, Structures of escherichia coli and lactobacilluscasei dihydrogolate reductase refined at 1.7 angstroms resolution. i.general features and binding of methotrexate, J. Biol. Chem., 257:13650,1982) of DHFR. No attempts were made to optimize the structures withquantum or classical methods. Thus, the ring distortion and out-of-planebending as observed in the crystal structures were left intact. Hydrogenatoms were added using Cerius2 (Program Cerius2, distributed byMolecular Simulations Inc., 9685 Scranton Rd. San Diego Calif.92121-3752).

Features were computed according to the parameters in Table III, asshown in FIG. 8. Placing scoops at atomic nuclei produced 53 scoops forDHF and 56 for MTX. Further, feature groups were defined using thefunctional-based classification scheme illustrated in FIGS. 7(A) and7(B). These group definitions are somewhat similar to those defined in aQSAR study of DHFR inhibitors by Hopfinger (William J. III Dunn, AntonJ. Hopfinger, Cornel Cantana, and Chaya Duraiswami, Solution of theconformation and alignment tensors for the binding of trimethoprim andits analog to dihydrofolate reductase: 3d quantitativestructure-activity relationship study using molecular shape analysis,3-way partial least squares, and a 3-way factor analysis, J. Med. Chem.,39:4825 4832, 1996). The definitions emphasize regions of the moleculeimportant for binding and avoid features from parts of the structuresthat appear unessential for activity.

The loadings of the two Fisher discriminants derived from the functionalgrouping are shown in FIG. 9 (e.g., the Fisher discriminant matrix W(see, e.g., equation (23))). As shown in FIG. 9, W represents the linearmapping from the 16-dimensional local scoop descriptors (as describedabove) to the 2-dimensional discriminant space in which the similaritymeasure is defined. In order to make the components W_(kj) comparable,they have been multiplied by the standard deviation σ_(k) of the k-thdescriptor (k=1, . . . , 16), sampled over the total pool of features.

Further, the first discriminant has domain loadings in Q_(xx) andQ_(yy), as well as the inertial J_(y) and J_(z) components of thefeature. Large Q components with the present property field arise whenthe differences in electronegativity with respect to the average liefurther from their center of dipole. The second discriminant is mostsensitive to M, the integral of the electronegativity property fieldover the scoop, and differences in J_(z) from J_(x) to J_(y), which maybe seen as a crude measure of planarity of field within the scoop.Differing training sets will lead to a different feature weighting indiscriminant space.

The atom-centered features of both DHF and MTX, once projected onto theFisher discriminants resulting from the functional grouping, arepartitioned into bins. The size of the bins in each dimension is set tofour times the standard deviation of the largest group.

The resulting partitioning scheme is shown in FIG. 6 and Table IV inFIG. 10. As shown in Table IV, to define similarity, the discriminantspace depicted in FIG. 6 is partitioned into rectangular bins. Each bincorresponds to a cell in the table. The features are labeled by the nameof the central atom of the corresponding scoop (e.g., DHF, MTX), asshown in FIGS. 11(A) and 11(B). In other words, the feature labels referto the atoms on which the feature scoops were centered.

Specifically, FIG. 11(A) illustrates dihydrofolate, and FIG. 11(B)illustrates methotrexate with atom numbers shown. Inspection of thegrouping reveals the features of the designated groups are in factclustered in the same region of discriminant space. However, rectilinearquantization has its problems. There is no easy way with this method tosegregate all of the desired features together in distinct bins.

DHF has 53 atoms, so with scoops located on atomic centers, this resultsin 53 features. However, 6 features fail to pass the threshold forsufficient non-degeneracy and are removed. For the construction ofcorrespondences between the query and database features, multiplefeatures are generated for scoops in the query molecule (DHF) that lacksufficient asymmetry to define the sense of their internal axes. Thisresults in the addition of 25 more features for DHF, for a total of 72.Of the 56 scoops for MTX, 10 fail to pass the threshold for sufficientnon-degeneracy, leaving 46 features. The total number of correspondenceswithout grouping is therefore the product of the number of features inDHF and MTX, or 72*46=3312, as shown in Table V.

Specifically, Table V in FIG. 12 illustrates the distribution of thecorrespondence cluster sizes for rigid body superposition of the crystalstructure of MTX onto that of DHF. In the left column, features were notgrouped, all query features were corresponded to all database features.The right column sets forth the functional feature grouping, where onlysimilar features were corresponded. Note that with the functionalgrouping, the total number of correspondences is only 194. In otherwords, the total number of correspondences with grouping is only aboutone twelfth of the number without grouping, resulting in a significantdecrease in computer time. While the cluster size distribution suggeststhat the grouping eliminates a number of those correspondences that wentinto the large clusters in the all-to-all case, detailed inspection ofthe individual high-voting clusters shows that the same alignments areproduced in both cases.

Therefore, it can be seen that, in spite of its problems, a partitioningof discriminant space may be necessary. A brute force comparison of allquery features with all candidate features will likely becomeprohibitively expensive from a computational perspective when applied tolarger problems. Furthermore, examination of the large clusters in thefull correspondence case (e.g., see Table V in FIG. 12) indicates thatnoise from spurious members in these clusters contaminates the averagetransformation of the clusters. Ill-defined transformations from suchclusters lead to alignments where few structural elements are alignedwell.

In both groupings, when one passes the clusters to the assembler (whichin this case may only apply shape screens and scoring since themolecules are already assembled), essentially the same alignmentsresult. This will not be the case when considering the flexibility ofMTX. An important point to emphasize here, is that by injecting relevantknowledge into the feature classification scheme, one arrives at theanswer with less work. This point becomes important when largerdatabases of molecules with more conformational degrees of freedom areconsidered. This is more than a timing issue: in practice, one oftenmust apply cutoffs and limits to the search. Arriving at an answerefficiently at a small scale may sometimes translate into whether onesees it at all at a larger scale.

A result that is fairly robust with respect to choice of clusteringparameters is the production of two alignments, one where the benzamiderings are aligned, and the other with the observed crystallographicalignment of the pteridine rings indicating superposition of the regionsof the molecules that bind to DHFR. The presence of these two alignmentsstems from two origins in conflict. One alignment arises from thestrength of an exact substructural match, namely the p-amino-benzamide.The other, which is the experimentally observed alignment of thepteridine rings, is due to the similarity in locations of chemicalfunctional groups.

Balancing how exact substructural matches should be weighted withrespect to similarity in functional group definition is an issue thatmust be dealt with in any superposition algorithm or similarity scoringfunction. Exact substructure matches are sometimes relevant, even iftrivial. One certainly could not fault an algorithm for scoring such acorrespondence high. Rather, one must balance the relative importanceexact substructural matches have with respect to similar substructures.Since there is no universal answer, this should be addressed by thecontext. In this case (e.g., DHF and MTX), the two form separate anddistinct clusters in transformation space, and are thus presented asalternative alignments.

Flexible Superposition

To query DHF against a database that represents the full conformationalspace of MTX, the MTX structure was fragmented, and the conformations ofeach fragment and fragment pair were tabulated. The fragmentation isillustrated in FIG. 2, which also shows that the conformationalresolution was 60° for the five single bonds and 180° for the anilinebond. Fragment conformers and fragment pairs that are produced usingthese angle resolutions were analyzed for the presence of non-bondedatom pairs that are closer than 1.7 Å, and these conformations wereeliminated from the tabulation (Note that the value of 1.7 Å chosen forthe bump check parameters used in this work is rather small. Therefore,some high energy conformations are used as fragment pairs and also somehigh energy candidates are produced during assembly. The value waschosen to screen out only the worst cases of steric overlap in order toassess the method with a larger work load. The performance of the methodimproves if this parameter is increased.).

The non-bonded atom threshold reduces the number of conformers offragment C from 36 to 27, the number of A-B fragment pairs from 72 to48, and the number of B-C fragment pairs from 324 to 234. The list ofinter-fragment torsion angles is appended to the original angle presentbefore fragmentation. The results are shown in Table VI in FIG. 13.

Specifically, Table VI shows the statistics for the fragment andfragment pair partitioning of MTX. The 35 fragment conformers and 284rotatable bond edge records allow for the representation of more than15,500 full molecular conformations (e.g., see equation (1)). Thus, oneof the 49 A-B fragment pairs and one of the 235 B-C fragment pairs hasthe original angle found in the crystal structure.

The cluster distributions in Table VII in FIG. 14 show the importance ofinjecting relevant context into the classification scheme. Specifically,Table VII shows the distribution of the correspondence cluster sizes forflexible superposition of MTX onto the crystal structure of DHF. Themiddle column refers to features that were grouped according to theelement of the atom at the center of the scoop (e.g., C, O or N). Theright column refers to features that were grouped according to thechemical function of the molecular region in which the scoop is defined.The two grouping schemes imply different similarity measures. Animportance of a cluster is given by the number of its members, a largernumber indicating more correspondences consistently supporting the samealignment. The total number of correspondences following from functiongrouping is only about half the number of correspondences from elementalgrouping, which results in a significant decrease in workload by theclustering algorithm.

Thus, as can be seen from the total number of correspondencesconstructed in each case, the work load of the correspondence step ismarkedly higher for the elemental grouping scheme than in the functionalgrouping scheme. Inspection of the partitioning of the elementalgrouping revealed a decidedly less rational distribution. Bins wereoccupied with more random groupings of features compared to thefunctional scheme.

Furthermore, there is a difference in the types of alignments of thefragment pairs containing the p-amino-benzamide ring and the pteridinering that are produced by the two scheme. In the functional groupingscheme we see three types of alignments: one with the p-amino-benzamidering of MTX tightly aligned onto that of the DHF; one with the pteridinering of MTX tightly aligned onto that of DHF in a way compatible withthe DHFR binding implied by the crystal structures; and one with thepteridine ring of MTX tightly aligned onto that of DHF in a waycompatible with good steric overlap of the rings.

In contrast, with the element grouping scheme we see only alignmentswhere the p-amino-benzamide ring of MTX is tightly aligned onto that ofthe DHF. With the set of parameters shown in Table III of FIG. 8, tightalignments of the pteridine rings are not observed, although they can beproduced by varying the parameters of the clustering. Not surprisingly,it appears that with the element grouping scheme, the ability torecognize an exact substructural match on the p-amino-benzamide ring isgreater than the ability to recognize either a functional group orsteric match of the pteridine rings.

It should be added, however, that even with the element grouping scheme,although alignments based on superposition of the pteridine ring of MTXonto that of DHF are not observed, both the binding mode and stericoverlap orientations of the pteridine ring can be seen. However, thesealignments are produced by correspondences from regions of the moleculesaway from the pteridine ring and happen to survive shape screening inthe assembly phase.

All clusters with votes of five or more are used to produce the startingbases of the assembly step. Since, for this example, completed moleculesof MTX are produced when two fragment pairs are merged, the assemblyphase completes after one iteration.

Table VIII in FIG. 15 shows the work load of the different phases of theassembly process. Specifically, Table VIII shows the number of basesthat survive each assembly phase for the flexible superposition of MTXonto the crystal structure of DHF. The assembly step constructscandidate alignments from the local fragment pair alignments. For bothgrouping schemes, all clusters with five or more votes are consideredfor the assembly. Therefore, while the work load is similar for the twogrouping schemes, it will turn out that the quality of the producedcandidate is better with the functional grouping scheme.

The assembly phase produced 428 candidate alignments with the elementgrouping scheme and 436 with the functional grouping scheme. Allalignments were scored using the function of equation (32) and clusteredinto sets based on similarity of score and visual appearance. The scoresranged from 0.40 to 0.75. FIGS. 16-18 show three notable alignments fromthe three highest scoring sets formed from the 436 alignments thatresulted from using the functional grouping scheme.

Specifically, FIG. 16 shows a flexible alignment of MTX onto the crystalstructure of DHF generated with the inventive system 100. Most of thefeature correspondences that led to this alignment are around thearomatic rings. Therefore, this substructure is almost exactly aligned.The conformation of MTX is different from the one found in the crystalstructure. Thus, using the scoring function from equation (32), FIG. 16shows the highest scoring of the 436 alignments, with a score of Q=0.75.

Further, as shown in FIG. 16, the p-amino-benzamide rings are stronglyaligned and the aliphatic chains are actually aligned more closely thanis found from the two crystal structures. It is interesting to speculateabout why the chains were not observed in this conformation in thecrystal structures. Perhaps it can be attributed to the fact that 4dfris an E. Coli form and 1dhf is the human form of DHFR, and the twosequences differ in a nontrivial way, resulting in a different sitegeometry. Another reason might be that these chains are solvent exposed,and are thereby influenced by packing interactions from crystallizationof the complex. Of course, these kinds of considerations do not factorinto a superposition analysis because the enzyme is not considered.

While the alignments represented in FIG. 16 and FIG. 17 both stronglyalign the p-amino-benzamide rings, the pteridine rings are in oppositeorientations. In FIG. 16, the pteridine alignment is indicative of theobserved binding, whereas in FIG. 17, with a score of Q=0.63, thepteridine rings are in a sterically similar orientation.

Specifically, FIG. 17 also shows a flexible alignment of MTX onto thecrystal structure of DHF, which is mainly based on the aromatic ringsubstructure match. In contrast to FIG. 16, where the pteridine ringalignment agrees with the crystal structure, here the pteridine ring isflipped by 180°.

Further, due to the strong effect the benzamide has on the averagetransformation that aligned the respective fragment pairs, the correcthydrogen bonding groups on the pteridine ring are not as incident to thecorresponding groups on DHF as they are in the alignment shown in FIG.18, with a score of Q=0.62.

Specifically, FIG. 18 shows a flexible alignment of MTX onto the crystalstructure of DHF generated with the inventive system 100, which is basedon a similarity match of the pteridine ring, and it is the one closestto that implied by comparison of the two crystal structures. Note thatthis is not a substructure match. The planes of the aromatic rings areskewed with respect to each other. Of the three alignments shown, thisone has the best overlap of the pteridine ring, and is reasonably closeto the observed binding. This favorable pteridine ring alignment comesat the cost of the overlap of the benzamide ring.

The alignments produced by the element grouping scheme were similar tothose shown in FIG. 16 and FIG. 17.

Selectivity

It is important to consider how well the inventive system 100 worksusing these operating parameters when other molecules are added to thedatabase. Two groups of molecules will be added to the database: a groupof DHFR inactives and a second group of DHFR inhibitors. By comparingthe selectivity of MTX to the eight DHFR inactives the inventors firstexamined selectivity in a broad context. Examination of selectivity in afiner context will be conducted by comparing MTX to the eight DHFRinhibitors.

Table IX in FIG. 19 gives fragmentation statistics about the sixteenadditional molecules that were added to the database containing MTX. Theset for this experiment is comprised of eight inhibitors of DHFR andeight inhibitors of other enzymes indicated below, referred tocollectively as the DHFR inactives. The eight DHFR inhibitors arelabeled according to the compound number in Crippen's original work (G.M. Crippen, “Quantitative Structure Activity Relationships by DistanceGeometry: Systematic Analysis of Dihydrofolate Reductase Inhibitors”, J.Med. Chem., 23:599, 606, 1980).

The initial coordinates for the eight DHFR inhibitors shown in FIG. 20were obtained by energy minimization (The initial structures weregenerated using the user interface of the inventive system 100 and wereEnergy-minimized using the Dreiding force field (S. L. Mayo, B. D.Olafson, and W. A. Goddard III, Dreiding force field, J. Phys. Chem.,94:8897, 1990) with the Mulliken suite of programs (Mulliken 2.0: J. E.Rice, H. Horn, B. H. Lengsfield III, A. D. McLean, J. T. Carter, E. S.Replogle, L. A. Barnes, S. A. Maluendes, G. C. Lie, M. Gutowski, W. E.Rudge, P. A. Sauer, R. Lindh, K. Andersson, T. S. Chevalier, P.-O.Widmark, D. Bouzida, J. Pacansky, K. Singh, C. J. Gillan, P. Carnevali,W. C. Swope, B. Liu, IBM Almaden Research Center, San Jose, Calif.,1996).

Specifically, FIG. 20 shows the sixteen additional structures added tothe database containing MTX. Each of the DHFR inactives structures wereextracted from the PDB source file indicated (e.g., the eight DHFRinactives are ligands whose coordinates were extracted from PDB files ofthe ligand bound to a protein). Four are Thermolysin inhibitors (fromthe PDB files 1tlp, 1tmn, 3tmn, 5tmn), two are Carboxypeptidaseinhibitors (1cbx, 7cpa), and the remaining two are GlycogenPhosphorylase inhibitors (3gpb, 4gpb).

Though small, this group exhibits important features. The size on theinactive range from the small and rigid sugars that are GlycogenPhosphorylase inhibitors, to the larger flexible Thermolysin inhibitors.The size of the eight DHFR inhibitors are consistently smaller than MTX,and their activity spans a wide range (G. M. Crippen, Quantitativestructure activity relationships by distance geometry: Systematicanalysis of dihydrogolate reductase inhibitors, J. Med. Chem., 23:599606, 1980), as shown in the last column of Table X in FIG. 21.

Specifically, FIG. 21 shows each molecule's distribution ofcorrespondence cluster sizes for fragment pair alignments. Selectivityfor MTX with respect to the eight DHFR inactives is illustrated. This isa direct consequence of the choice of property field and contextualscaling provided by the functional grouping scheme. Selecting thehighest ranking transformation clusters, such as all those with at leastsix correspondences, across all molecules almost exclusively selects MTX(4dfr) for assembly.

Using a torsion angle resolution consistent with the methotrexatecharacterization described above, the number of conformationsrepresented ranges from a few dozen to over 10 million for the DHFRinactives. The number of conformations represented for the DHFRinhibitors total under a thousand for the set, due to their limitedflexibility. Thus, with a fairly small set of molecules, the inventorscreated a virtual conformational database where the DHFR inhibitors arehighly under-represented.

The inventors used the same conditions as were described above (e.g.,“Example: Application of the Present Invention to Dihydrofolate andMethotrexate”). All single bonds were sampled at 60° intervals. Terminalgroups such as carbody, isopropyl, and phenyl were left rigid. Amideswere left in a trans configuration. All property field settings wereused as specified in Table III in FIG. 8.

Ligands from 1tlp, 1tmn, 7 cpa, and 5tmn were partitioned into fourfragment nodes; and the ligands from 3tmn, 1cbx, 3gpb, 4gpb, and theeight DHFR inhibitors were partitioned into two fragment nodes.

It should be noted that the atom numbering for the non-hydrogen atomswas kept the same as in the corresponding pdb files. For the ninemolecules studied, the bonds that were cut to define fragments are asfollows (pdb label: {(atom number)-(atom number), . . . }): 1cbx: {3 5},1tlp: {1 2, 15 16, 23 24}, 1tmn: {1 13, 14 15, 22-25}, 3tmn: {8-9},5tmn: {12-13, 17-18, 24-25}, 7cpa: {9-10, 18-41, 23 26}, 3gpb: {1 7},4gpb: {1 7}, and 4dfr: {11 12, 24 25}. The internal torsional anglesthat were rotated are as follows: 1cbx: {2-3, 5-6}, 1tlp: {2-12, 16 17,16 19, 27 28, 24 27} 1tmn: {1 2, 2 3, 13 14, 14 17, 21 22, 25 26}, 3tmn:{12-13, 9-12, 2-3}, 1tmn: {3-4, 11-12, 16-17, 17-20, 25-28}, 7cpa {2324, 36 41, 18 40, 10 11, 10 39, 2 32}, 3gpb: {5 6}, 4gpb: {5 6}, and4dfr: {9-13, 14-19, 25-29, 29-30}. All angles were sampled at 60° withthe exception of 14 19 in 4dfr, which was sampled at 180°. For theadditional DHFR eight inhibitors, the structural parameters of C—S—Cgroups in molecules 2 and 67 were constrained to the experimental valuesof CS bond lengths and CSC bond angles in dimethylsulfide. Structuralparameters of C—SO2-C groups in molecules 1, 4 and 68 were constrainedto the experimental values of CS and SO bond lengths and CSC, CSO andOSO bond angles in dimethylsulfone (David R. Lide, Cre handbook ofchemistry and physics, 75.sup.th edition, 1994. pg. 9-31).

The fragmentation statistics for the sixteen molecules are shown alongwith those for methotrexate in Table IX in FIG. 19. In this table,except for methotrexate (4dfr) the approximate number of conformersrepresented is simply the number of torsional angles represented foreach bond (in this case 6, since the torsional angle resolution is 60°)raised to the number of rotatable bonds. Ethyl groups in esters 61 and64 where held fixed in an extended conformation. For methotrexatestatistics, see the above discussion in Table VI (FIG. 13) and Equation(1). Note that this represents only approximately the number ofconformers because some, sterically forbidden, are removed by the bumpcheck, and others are added, corresponding to the inter-fragment torsionangles present in the original crystal or energy minimized structures.

The number of fragment pairs is the number that have passed a bump checkof 1.7 Å. Features were computed at each atom center for each fragmentpair. One can see from the data in the table that there are considerablesavings in breaking the larger structures up and characterizing fragmentpairs rather than molecular conformations. Due to the singlepartitioning of the DHRF inhibitors, only the bump checks reduced thenumber of fragment pairs used for feature extraction.

Feature computation can be expensive, but it may only have to beperformed once, when molecular information is added to the database. Itscost will vary widely depending on complexity of the field computationand grid resolution, if the field is computed on a grid. Once thefeatures are computed, however, timings for the alignment and assemblystages of a query are independent of the field complexity. Featurecomputation with the property field as discussed above, and operationalsettings averaged about 4 features on a workstation (The timings wereproduced running the program of an IBM RS/6000 43P Model 260workstation, which has a Power3 CPU running at 200 and a 4 MB L2 Cache).

Selectivity During Alignment Stage

It is important for the efficiency and scalability of the method thatthe burden on the assembly stage is kept to a minimum. The results shownin Tables X, XI, XII and XIII (FIGS. 21-24, respectively) indicate aconsiderable degree of selectivity before the assembly stage for MTX andthe eight DHFR inhibitors relative to the DHFR inactives. The featureclassification scheme selects which correspondences will be made. Thereare a total of 542,981 features in the database, and 72 features on thequery molecule. This gives 39,094,632 possible correspondences. Usingthe functional grouping scheme, and screening out degenerate features,only 1,421,086 or about 3.7% of the total possible correspondences, wereconsidered for MTX and the eight inactives.

If the other eight inhibitors are included, this number only rises to1,458, 843. The correspondences of MTX and the eight inhibitors are only0.19% of the total. Each correspondence has an associated transformationwhich is clustered as described above. Clustering produced 1,053,312transformation clusters in total. These transformation clusters areranked according to the number of correspondences they contain. Fromthis pool of transformation clusters, each of which describes a fragmentpair aligned on the query molecule, one can select for assembly eitherthe top ranking clusters from each molecule, or the top ranking clustersfrom the entire pool of clusters. For either choice, one sees a highdegree of selectivity for MTX, which has been achieved by the choice ofproperty field and functional grouping scaling scheme.

Table X (FIG. 21) and FIG. 25 illustrate the selectivity of DHF for MTXwith respect to the eight inactives in the database. Table X shows eachmolecule's distribution of correspondence cluster sizes for alignmentsof its fragment pairs onto DHF. Selectivity for MTX with respect to theeight DHFR inactives is illustrated. This is a direct consequence of thechoice of property field and contextual scaling provided by thefunctional grouping scheme. Selecting the highest ranking transformationclusters, such as all those with at least six correspondences, acrossall molecules almost exclusively selects MTX (4dfr) for assembly.

FIG. 25 gives the corresponding proportions from each of the eightinactives and MTX for each cluster size. Specifically, FIG. 25 is a 100%stacked bar chart, derived from Table X in FIG. 21, for the proportionof transformation clusters for each cluster size for each of the eightinactives and MTX (4dfr). One sees that for small cluster sizes,transformations of fragment pairs from MTX represent a small fraction ofthe total number of cluster of that size. For the larger clusters,however, transformations involving MTX dominate. Selecting the largestclusters for assembly, therefore, almost exclusively focuses resourceson MTX.

As shown in FIG. 21, excluding the set of eight DHF inhibitors, therewere 1,421,086 feature correspondences. Only 35,037, or 2.5% of themwere from MTX. Similarly, this gives 1,036,401 transformation clusters,of which only 20,451, or 2.0% were from MTX. However, if one considersonly the larger clusters, which represent more significant alignments,one sees that MTX quickly dominates the distribution. For example, ifone selects clusters with six or more transformations from the entirepool of transformations, MTX represents 405 of the 533, or 76%; seven ormore gives 170 out of 190 or 89%; and eight or more exclusively selectsMTX.

Thus, even though MTX represents a small fraction of the totalcorrespondences considered, clustering clearly reveals MTX fragmentpairs as the best ones to use in the assembly stage. Subsequent assemblyof these MTX fragment pairs leads to the results seen in the previoussections. The additional 23 million conformations represented by the 13thousand fragment pairs of the molecules in FIG. 20 do not affect theresult that MTX is primarily selected from the database.

Table XI in FIG. 22 shows the corresponding results for the DHFRinhibitors. Specifically, Table XI illustrates selectivity for the DHFRinhibitors with respect to DHFR inactives by comparison with Table X(FIG. 21). Note that although correspondences involving the inhibitorsform larger clusters than inactives, such correspondences are still lessfavored than MTX (4dfr). Inspection reveals that clusters greater than 6are mainly due to the alignment of the flexible chain and benzamidegroups. This part of DHF and MTX is mostly solver exposed, as seen inthe crystal structures. Corresponding structure that would have occupiedthe same space is not present in the eight inhibitors.

Further, as seen in Table XI, despite the low number of conformationsrelative to the inactives, the DHFR inhibitors scored consistently highand were within the selection threshold of 6 votes of higher. Athreshold of 6 or more reduces the number of alignments forconsideration to 606,478 of which are from the inhibitor set (includingMTX). Even with a threshold of 5 votes or higher, the number ofalignments to consider is 5,221, 1, 031 being from the inhibitor set.This is out of the 1,061,703 total clusters.

Selection of the larger clusters for assembly therefore appears to be avalid means of significantly reducing the aligned fragment pairs priorto assembly. Given the elementary level of consideration for medicinalchemistry, the dramatic reduction in the number of clusters to consideris encouraging. It is clear that such specific pre-screening isessential for larger datasets, particularly when the final scoringfunction used is expensive.

Selectivity During Assembly Stage

If, however, the top ranking transformation clusters from each moleculeare considered individually, it is interesting to see whether there willstill be selectivity for MTX. Table XII in FIG. 23 shows the timing andload data for the assembly of the fragment pairs MTX and the eightinactives. Specifically, Table XII shows the alignment and assemblytimings (The timings were produced running the program of an IBM RS/600043P Model 260 workstation, which has a Power3 CPU running at 200 MHz anda 4 MB L2 Cache), the top Carbo scores, and the total number ofcandidates for each ligand investigated. The statistics are for the caseof flexible alignment of the eight inactives and MTX onto the DHF querymolecule. The initial alignments for each molecule represent those fromthe largest clusters.

Table XIII in FIG. 24 gives the data for the eight inhibitors.Specifically, Table XIII shows the alignment and assembly timings (As inTable XII, here the timings were produced running the program of an IBMRS/6000 43P Model 260 workstation, which has a Power3 CPU running at 200MHz and a 4 MB L2 Cache), the top Carbo scores, and the total number ofcandidates for the eight DHFR inhibitors investigated. All structures inthis series had only one fragment pair, so no merging was required. Thelast column on the right is the experimental binding energy.

Based on the size of the transformation clusters, the top rankingfragment pair alignments were selected for each molecule separately. Foreach molecule, enough cluster sizes were considered to yield at least500 fragment pair alignments. This resulted in the number of initialalignments shown in Table XII (FIG. 23) and Table XIII (FIG. 24).

Thus, it can be seen that the bulk of the time for the Thermolysin andCarboxypeptidase inhibitors is spent indexing features and clusteringtransformations during the alignment stage, where most of the potentialassembly load is screened out. For MTX, however, most of the time isspent on assembly due to the large number of fragment pair alignmentsthat could be merged, screened for shape and scored. All assembly runswere exhaustive for the selected fragment pairs.

The assembly results again strongly favor MTX over any of the othermolecules investigated. Most of the molecules did not have sufficientsimilarity to DHF for a complete assembly of the molecule. In fact, onlyMTX showed any merges of fragment pairs. For those molecules that hadopportunities to merge, fragment pairs must be placed such that thecommon fragments are proximal enough to be merged. For molecules whereonly a small part is similar to the DHF query, the assembly stage willyield as candidates the fragment pairs or partial assemblies aligned tothe corresponding query regions. This is the case in Table XII (FIG. 23)and all of Table XIII (FIG. 24) where molecules without any countedmerges still produced candidates. Assembling complete conformersrequires the combination of high ranking fragment pairs and theirproximal placement.

Alignments must also pass a shape screen in order to qualify ascandidates and be scored. One can see from Table XII (FIG. 23) that forthree of the molecules, not only were there no merges of fragment pairs,but none of the initial alignments were sufficiently contained withinthe volume of the query molecule to make it past the shape screen. Thus,despite the flexibility of these molecules, only a small number ofcandidates were submitted for scoring. Table XIII (FIG. 24) shows all ofthe eight inhibitors had alignments of conformers that passed the shapescreen.

The last column of Table XII (FIG. 23) shows the highest Carbo scores ofthe candidates produced by the assembly stage. It can be seen, however,that of the few candidate conformer alignments submitted for finalevaluation, the Carbo score ranks MTX well above the other. The fourmolecules from 3tmn, 1cbx, 3gpb, and 4gpb are complete as a singlefragment pair, and so no assembly is required. Their difference in sizeand shape from DHF results in a much lower Carbo score. It should beemphasized here that there except for MTX and these four molecules, andthe eight inhibitors, the Carbo scores represent the evaluation ofalignments of partially assembled molecules.

Inspection of the alignments of the DHFR inhibitors reveal that in eachcase, the binding mode corresponding to MTX is observed (e.g., see FIGS.16, 17 and 18). Compounds 2 and 6 have an Hbond acceptor that allows abinding mode analogous to DHF, which is observed. In each case the topalignments are adequately placed to relax into a corresponding bindingmode.

As noted above, Table XIII (FIG. 24) shows the assembly results for theset of eight DHFR inhibitors. They are represented by a single fragmentpair due to their limited flexibility, so no merging step was required.The shape screen was the only checkpoint that was applied to theinhibitors. Since the shape evaluation is simply the Carbo score, noconsiderations relevant to medicinal chemistry beyond shape were madefor this example (e.g., consideration of functional group compatibility,as in SQ (Michael D. Miller, Robert P. Sheridan, and Simon K. Kearsley,“Sq: A Program for Rapidly Producing Pharmacophorically RelevantMolecular Superpositions”, J. Med. Chem., 42:1505-1514, 1999)).

One of the alignments of 3tmn has a Carbo score of 0.54. This is theonly compound with a comparable Carbo score to the DHFR inhibitors.Inspection of this alignment, however, reveals that 3tmn is aligned tothe branched chain of DHF. Again, this could well be screened out byfilters favoring the known binding mode of DHFR inhibitors, since thebranched chain region is known from crystal structures to be solventexposed. This is also the case with the alignments observed with thesugars 3gpb and 4gpb.

A further note on the lower scores of the DHFR inhibitors is that theCarbo score penalizes for any mismatched shape. When aligned correctlyto DHF, the DHFR inhibitors have no corresponding structure to fill thevolume corresponding to the chain of DHF. This is reflected in thescores of the best alignments, which are around 0.5.

Even though the inventors selected the top ranking fragment pairalignments for each molecule, fragment pairs did not match across theentire volume of the query, so there were not multiple fragment pairs tobe considered for merging to form more complete conformers (and,therefore, higher scoring candidates) for molecules other than MTX.

The structure of DHFR was not used at any phase of the screeningprocess, since this is a similarity searching application. It is not ourintention here to further refine or optimize the binding mode. Ourresults show that from a modest flexible dataset, we are able to reducethe number of conformation and alignments to a few hundred, from severalmillion.

In summary, the inventive system 100 offers a systematic way to usearbitrary property fields for the purposes of similarity search andalignment. Context specific information can be used to scale therelative importance of high dimensional descriptors derived from theproperty field under study. The system 100 may be designed to operate onoverlapping parts, or fragment pairs, of molecules, and utilizes anefficient method of conformational space representation.

The inventors applied the inventive system 100 to the benchmarkdihydrofolate-methotrexate system, and have demonstrated that byinjecting context specific knowledge into the feature classificationscheme, one arrives at the reasonable alignments more efficiently. Forthis study, the inventors used a very simple property field. Even withthis simple property field the appropriate inclusion of context in thedefinition of similarity allowed the production of alignments consistentwith the binding modes present in the crystal structures in both rigidand flexible treatments of conformational space.

Further, the inventors looked in detail at how the inventive system 100works in performing a query for alignments on dihydrofolate from adatabase of seventeen molecules representing approximately 23 millionconformations. The inventive system 100 exhibits a high degree ofselectivity for alignments of methotrexate and as well as other DHFRinhibitors. The selectivity is apparent at initial alignment andassembly stages, and is reflected in the resulting Carbo scores.

Referring again to the drawings, FIG. 26 illustrates an inventivefield-based similarity search method 200 according to the presentinvention. As shown in FIG. 26, the inventive method 200 includesgenerating (210) a conformational space representation and an arbitrarydescription of a three-dimensional property field for a flexiblemolecule, characterizing (220) parts of the flexible molecule andrepresenting a query molecule using the arbitrary description for acomparison with the conformational space representation, and aligning(230) the parts to the query molecule and assembling the parts to forman alignment onto the query molecule.

Referring again to the drawings, FIG. 27 illustrates a typical hardwareconfiguration which may be used for implementing the inventivefield-based similarity search system and method. The configuration haspreferably at least one processor or central processing unit (CPU) 311.The CPUs 311 are interconnected via a system bus 312 to a random accessmemory (RAM) 314, read-only memory (ROM) 316, input/output (I/O) adapter318 (for connecting peripheral devices such as disk units 321 and tapedrives 340 to the bus 312), user interface adapter 322 (for connecting akeyboard 324, mouse 326, speaker 328, microphone 332, and/or other userinterface device to the bus 312), a communication adapter 334 forconnecting an information handling system to a data processing network,the Internet, and Intranet, a personal area network (PAN), etc., and adisplay adapter 336 for connecting the bus 312 to a display device 338and/or printer 339. Further, an automated reader/scanner 341 may beincluded. Such readers/scanners are commercially available from manysources.

In addition to the system described above, a different aspect of theinvention includes a computer-implemented method for performing theabove method. As an example, this method may be implemented in theparticular environment discussed above.

Such a method may be implemented, for example, by operating a computer,as embodied by a digital data processing apparatus, to execute asequence of machine-readable instructions. These instructions may residein various types of signal-bearing media.

Thus, this aspect of the present invention is directed to a programmedproduct, including signal-bearing media tangibly embodying a program ofmachine-readable instructions executable by a digital data processor toperform the above method.

Such a method may be implemented, for example, by operating the CPU 311to execute a sequence of machine-readable instructions. Theseinstructions may reside in various types of signal bearing media.

Thus, this aspect of the present invention is directed to a programmedproduct, comprising signal-bearing media tangibly embodying a program ofmachine-readable instructions executable by a digital data processorincorporating the CPU 311 and hardware above, to perform the method ofthe invention.

This signal-bearing media may include, for example, a RAM containedwithin the CPU 311, as represented by the fast-access storage forexample. Alternatively, the instructions may be contained in anothersignal-bearing media, such as a magnetic data storage diskette 400 (FIG.28), directly or indirectly accessible by the CPU 311.

Whether contained in the computer server/CPU 311, or elsewhere, theinstructions may be stored on a variety of machine-readable data storagemedia, such as DASD storage (e.g., a conventional “hard drive” or a RAIDarray), magnetic tape, electronic read-only memory (e.g., ROM, EPROM, orEEPROM), an optical storage device (e.g., CD-ROM, WORM, DVD, digitaloptical tape, etc.), paper “punch” cards, or other suitablesignal-bearing media including transmission media such as digital andanalog and communication links and wireless. In an illustrativeembodiment of the invention, the machine-readable instructions maycomprise software object code, complied from a language such as “C,”etc.

With its unique and novel features, the present invention provides afast and efficient field-based similarity search system and method whichare not confined to a particular field definition. For example, theinventive system and method may be designed for simplistic,phenomenological fields, as well as for fields derived from quantummechanical calculations. Therefore, the claimed system and methodprovides improved versatility over conventional systems and methods.

While the invention has been described in terms of preferredembodiments, those skilled in the art will recognize that the inventioncan be practiced with modification within the spirit and scope of theappended claims.

What is claimed is:
 1. A field-based similarity search system,comprising: an input device which inputs a query molecule; and aprocessor which: partitions a conformational space of said querymolecule into a fragment graph comprising an acyclic graph includingplural fragment nodes connected by rotatable bond edges; computes aproperty field on fragment pairs of fragments of said query moleculefrom said fragment graph, said property field comprising a localapproximation of a property field of said query molecule; constructs aset of fragment pairs for description of each candidate molecule whereineach set is known as a set of candidate molecule fragment pairs;constructs a set of features of said fragment pairs based on saidproperty field, said features comprising a set of local, rotationallyinvariant, and moment-based descriptors generated from all conformationsof said fragment graph of said query molecule; and weights saiddescriptors according to importance as perceived from a training set ofdescriptors to generate a context-adapted descriptor-to-key mappingwhich maps said set of descriptors to a set of feature keys comprisingindices that label grid cells in discriminant space, wherein a candidatemolecule fragment pair is within a set of candidate molecule fragmentpairs that describe a candidate molecule stored in a feature database tosaid query molecule, and wherein the number of candidate moleculefragment pairs in the set, C_(fp), is given byC_(fp)=(n−1)×(C_(frag))²×C_(rbe), where n is the number of fragments insaid candidate molecule and n−1 is the number of rotatable bond edgesconnecting n fragments, C_(frag) is a number of conformations in afragment of said fragments and C_(rbe) is a number of steps in whichsaid rotatable bond edges are sampled.
 2. The field-based similaritysearch system of claim 1, wherein said processor further: alignsfragment pairs of the candidate molecule stored in the feature databaseto said query molecule.
 3. The field-based similarity search system ofclaim 2, wherein said processor further: assembles said alignedcandidate molecule fragment pairs to construct a full aligned candidatemolecule.
 4. The field-based similarity search system of claim 3,further comprising: a display device for displaying said full alignedcandidate molecule.
 5. The field-based similarity search system of claim1, wherein said processor partitions said conformational space byselecting of a set of bonds in said molecule to cleave.
 6. Thefield-based similarity search system of claim 1, wherein said processorfurther partitions said conformational space by constructing a datarepresentation in the fragment graph, each node of the fragment graphcomprising plural fragment nodes connected by rotatable bond edges, aspecific conformation of a fragment node in said plural fragment nodescomprising a fragment of said query molecule, and two neighboringfragments connected by a rotatable bond at a specific dihedral anglecomprising said fragment pair.
 7. The field-based similarity searchsystem of claim 6, wherein said processor constructs said set offeatures by partitioning a volume occupied by said query molecule bydefining a set of overlapping scoops and local property fieldsassociated with said overlapping scoops, said descriptors comprisingvector and tensor quantities which are expressed in terms of an internalcoordinate system, such that the descriptor is independent of alaboratory frame.
 8. The field-based similarity search system of claim7, wherein said processor aligns said candidate molecule fragment pairsby identifying a scoop for said candidate molecule which has a featurekey which matches a feature key from said set of feature keys for saidquery molecule, to determine correspondences between a query moleculefragment pair feature from said set of features of fragment pairs ofsaid query molecule and a fragment pair feature of said candidatemolecule.
 9. The field-based similarity search system of claim 8,wherein said processor aligns said candidate molecule fragment pairsfurther by clustering said correspondences using a pose clusteringmethod, the correspondences within a cluster referring to a fragmentpair.
 10. The field-based similarity search system of claim 9, whereinsaid processor aligns said candidate molecule fragment pairs further byselecting a cluster from said correspondence clustering, calculating anaverage transformation for said selected cluster, and applying saidtransformation to coordinates of the fragment pair referred to by saidcluster to construct a set of hypotheses representing candidate moleculefragment pairs aligned on said query molecule.
 11. The field-basedsimilarity search system of claim 1, wherein said features of saidcandidate molecule fragment pairs and query molecule fragment paircomprise generalizations of comparative molecular moment analysisdescriptors.
 12. The field-based similarity search system of claim 1,wherein an entry of a hash table refers to a fragment pair of saidcandidate molecule and describes an internal frame associated with adescriptor of said set of descriptors.